Fatou Set: Information From Answers.com fatou set In mathematics , a fatou set is defined informally as the largest openset of fatou sets are named after French mathematician pierre fatou. http://www.answers.com/topic/fatou-set
Extractions: showHide_TellMeAbout2('false'); Business Entertainment Games Health ... More... On this page: Wikipedia Best of Web Mentioned In Or search: - The Web - Images - News - Blogs - Shopping Fatou set Wikipedia @import url(http://content.answers.com/main/content/wp/css/common.css); @import url(http://content.answers.com/main/content/wp/css/gnwp.css); Fatou set In mathematics , a Fatou set is defined informally as the largest open set of points on which iterations of a given map (or collection of maps) have relatively tame long-term behaviour, in the sense that points that start close together stay close together. A map's Fatou set is the complement of its Julia set Less commonly, the term Fatou set or Fatou dust is sometimes used to refer to a Julia set that is not connected Fatou sets are named after French mathematician Pierre Fatou This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see Best of the Web Some good "Fatou set" pages on the web: Math mathworld.wolfram.com
Fatou's Lemma: Information From Answers.com fatou s lemma fatou s lemma establishes an inequality relating the integral (in It is named after the French mathematician pierre fatou (1878 1929). http://www.answers.com/topic/fatou-s-lemma
Extractions: showHide_TellMeAbout2('false'); Business Entertainment Games Health ... More... On this page: Wikipedia Best of Web Mentioned In Or search: - The Web - Images - News - Blogs - Shopping Fatou's lemma Wikipedia @import url(http://content.answers.com/main/content/wp/css/common.css); @import url(http://content.answers.com/main/content/wp/css/gnwp.css); Fatou's lemma Fatou's lemma establishes an inequality relating the integral (in the sense of Lebesgue ) of the limit inferior of a sequence of functions to the limit inferior of the sequence of integrals of the functions. It is named after the French mathematician Pierre Fatou Fatou's lemma states that if f f , ... is a sequence of non-negative measurable ) functions, then Fatou's lemma is proved using the monotone convergence theorem Fatou's lemma is particularly useful in probability theory , in establishing results about the convergence of the expectations of the elements of a sequence of random variables . Suppose that the sequence of functions is a sequence of random variables, X X , ..., with
Extractions: Shopping Cart Table of Contents In 1920, Pierre Fatou expressed the conjecture thatexcept for special casesall critical points of a rational map of the Riemann sphere tend to periodic orbits under iteration. This conjecture remains the main open problem in the dynamics of iterated maps. For the logistic family x- ax(1-x), it can be interpreted to mean that for a dense set of parameters "a," an attracting periodic orbit exists. The same question appears naturally in science, where the logistic family is used to construct models in physics, ecology, and economics. In this book, Jacek Graczyk and Grzegorz Swiatek provide a rigorous proof of the Real Fatou Conjecture. In spite of the apparently elementary nature of the problem, its solution requires advanced tools of complex analysis. The authors have written a self-contained and complete version of the argument, accessible to someone with no knowledge of complex dynamics and only basic familiarity with interval maps. The book will thus be useful to specialists in real dynamics as well as to graduate students. Table of Contents Series: Annals of Mathematics Studies
Fatou's Lemma -- Facts, Info, And Encyclopedia Article link for more info and facts about pierre fatou) pierre fatou (1878 1929).fatou s lemma states that if f1, f2, is a sequence of (Click link for http://www.absoluteastronomy.com/encyclopedia/f/fa/fatous_lemma.htm
Extractions: var dc_UnitID = 10; var dc_PublisherID = 512; var dc_BackgroundColor1 = 'white'; var dc_BackgroundColor2 = 'white'; var dc_TitleColor = 'blue'; var dc_TextColor = 'black'; var dc_URLColor = 'blue'; var dc_URLVisitedColor = 'green'; var dc_sm_type = 'horizontal'; var dc_Width = 700; var dc_Height = 75; var dc_caption_font_bgColor = 'white'; var dc_caption_font_color = 'blue'; var dc_OutBorder = 'no'; var dc_adprod='TM'; [Categories: Real analysis] Fatou's lemma establishes an (Lack of equality) inequality relating the (The result of a mathematical integration; F(x) is the integral of f(x) if dF/dx = f(x)) integral (in the sense of (Click link for more info and facts about Lebesgue) Lebesgue ) of the (Click link for more info and facts about limit inferior) limit inferior of a (Serial arrangement in which things follow in logical order or a recurrent pattern) sequence of (A mathematical relation such that each element of one set is associated with at least one element of another set) function s to the limit inferior of the sequence of integrals of the functions. It is named after the French mathematician
Mandelbrot Set -- Facts, Info, And Encyclopedia Article 1905 by (Click link for more info and facts about pierre fatou) pierre fatou, fatou never saw the image of what we now call the Mandelbrot set as we http://www.absoluteastronomy.com/encyclopedia/m/ma/mandelbrot_set.htm
Extractions: In (A science (or group of related sciences) dealing with the logic of quantity and shape and arrangement) mathematics , the Mandelbrot set is a ((mathematics) a geometric pattern that is repeated at every scale and so cannot be represented by classical geometry) fractal that is defined as the (A group of things of the same kind that belong together and are so used) set of points c in the ((psychoanalysis) a combination of emotions and impulses that have been rejected from awareness but still influence a person's behavior) complex plane for which the (Click link for more info and facts about iteratively) iteratively defined (Serial arrangement in which things follow in logical order or a recurrent pattern) sequence
Biography-center - Letter F wwwhistory.mcs.st-and.ac.uk/~history/Mathematicians/fatou.html; Fauconnier,pierre-Michel www.grandprix.com/gpe/cref-faupie.html; Faulhaber, Johann http://www.biography-center.com/f.html
Extractions: random biography ! Any language Arabic Bulgarian Catalan Chinese (Simplified) Chinese (Traditional) Croatian Czech Danish Dutch English Estonian Finnish French German Greek Hebrew Hungarian Icelandic Indonesian Italian Japanese Korean Latvian Lithuanian Norwegian Polish Portuguese Romanian Russian Serbian Slovak Slovenian Spanish Swedish Turkish 448 biographies F asenmyer, Mary Celine
Extractions: sociologist, professor and researcher, Université de Paris Fatou Sow received her baccalaureate in science and philosophy from theUniversité de Dakar before leaving for France to complete a doctorate in sociology. This marked the beginning of a brilliant international career, which has taken her to three continents: Africa, Europe and North America. Attached to the Centre National de la Recherche Scientifique (CNRS) in Paris, Sow is among a first generation of researchers from less-developed countries who have given a voice not only to their own nations, but also to women and the disadvantaged. She was one of a group of African and Canadian social scientists who were among the first to study systematically the relationship between gender relations and the destruction and degradation of the natural environment in Africa. This capacity to recognize new and important research areas is a defining characteristic of her work. In her role as a teacher, Ms. Sow had inspired countless young people in Senegal and elsewhere. They have been impressed not only with her intellectual clarity, her vision for Senegal and Africa, her energy and enthusiasm, but also by her grace and dignity.
Mandelbrot Set And Fractals Gaston Julia and pierre fatou whilst extending it into higher order mappings . the work of Gaston Julia and pierre fatou during the First World War. http://ourworld.compuserve.com/homepages/pagrosse/mandelb.htm
Extractions: Fractals Fractals have always been interesting to people who like to explore but getting your hands on a program that will let you do that has always been a problem. The link at the bottom of this page allows you to download a copy of my mandelbrot program which is postcardware (you send me a post card to license it) Technical Mumbo Jumbo:- ) as well as a number of more esoteric fractals. Exploration is not limited to the x : i plane but extends to the y : z plane as well giving you Julia sets and Fatou Dusts reflecting the earlier work of the mathematicians Gaston Julia and Pierre Fatou whilst extending it into higher order mappings. Background Mumbo Jumbo:- E xisting between the -1 and +1 in four dimensions, the ginger bread man fractal figures of the Mandelbrot set (based on two of the planes, the x plane and the imaginary plane) have become familiar to us all.
Pierre Fatou Biography pierre fatou biography and related resources. pierre fatou (28 February 1878 10 August 1929) was a French mathematician working in the field of http://www.biographybase.com/biography/Fatou_Pierre.html
Extractions: Biography Base Home Link To Us Search Biographies: Browse Biographies A B C D ... Z Pierre Fatou Biography Pierre Fatou (28 February 1878 - 10 August 1929) was a French mathematician working in the field of complex analytic dynamics. He entered the École Normale Supérieure in Paris in 1898 to study mathematics and graduated in 1901 when he was appointed an astronomy post in the Paris Observatory. Fatou continued his mathematical explorations and studied iterative and recursive processes. Fatou was particularly interested in the case where Z0 = 0, which was later analysed with computers by Benoit Mandelbrot to generate graphical representations of the behaviour of this series for each point, c, in the complex plane - now popularly called the Mandelbrot set. If the series does not tend to infinity, it is in the Mandelbrot set otherwise it is not. Images of the set are typically coloured black where points are in the set and coloured according to the escape speed of the series where not. Fatou wrote many papers developing a Fundamental theory of iteration in 1917, which he published in the December 1917 part of Comptes Rendus. His findings were very similar to those of Gaston Maurice Julia, who submitted a paper to the Académie des Sciences in Paris for their 1918 Grand Prix on the subject of iteration from a global point of view. Their work is now commonly referred to as the Generalised Fatou Julia theorem.
Prisoners And Escapees--Julia Sets Discussion Let s talk about Prisoners and Escapees, and Gaston Julia and pierre fatou.After World War I, Julia and fatou were interested in iterating two variable (or http://www.shodor.org/interactivate/discussions/julia.html
Extractions: Prisoners and EscapeesJulia Sets Discussion Student: So the Mandelbrot set is made up of Julia sets , which are prisoner sets. What is a prisoner Mentor: That is a simplified description, but you have all the main ideas. Let's talk about Prisoners and Escapees , and Gaston Julia and Pierre Fatou. After World War I, Julia and Fatou were interested in iterating two variable (or complex) equations using recursion . They chose an equation and iterated it using various starting points. Mathematicians call this sort of problem a dynamical system . They found that if you looked at different starting points, different behaviors would emerge. Let's look at the simplest interesting case: f(Z) = Z^2 + C where C is any point (complex number) inside the circle of radius 2. We are only interested in those points because that is where we will be looking for the Mandelbrot set eventually. Here's an experiment to try: Let C = (0,0) and start with the point (0,1). What happens? Student: Let's see; Z = (0,1) f(0,1) = (0,1)^2 + (0,0) = (-1,0) + (0,0) = (-1,0)
History Of Astronomy: Persons (F) fatou, pierre Joseph Louis (18781929). Short biography and references (MacTutorHist. Math.) Faulkner, Don (20th c.) Very short biography http://www.astro.uni-bonn.de/~pbrosche/persons/pers_f.html
Extractions: Fabricius, David (1564-1617) Fabricius, Johannes (1587-1616) Fabry, Marie Paul Auguste Charles (1867-1945) Fairbank, William Martin (1917-1989) Fairfax Somerville, Mary: see Somerville, Mary Fairfax Greig (1780-1872) Falck, Anders (1740-1796) Faraday, Michael (1791-1867) Fatou, Pierre Joseph Louis (1878-1929) Faulkner, Don (20th c.) Fermat, Pierre de (1601-1665) Biography Short biography and references (MacTutor Hist. Math.)
Mandelbrot And Julia Sets Gaston Julia (18931978) and pierre fatou (1878-1929) made a fundamental contributionto the study of iterative processes. Their contribution (Ref 3), http://www.cut-the-knot.com/blue/julia.shtml
Extractions: Sites for parents (An index may have a content of its own.) Given a function f(x) and a starting value x one can construct a new value x =f(x ). With some persistence, the next value x is obtained by another application of f: x =f(x )=f(f(x )). This is an iterative process that, generally speaking, generates a sequence x , x , ... x k , ..., where x k is the k th iterate obtained by applying the function f to x k times. The sequence is known as an orbit of its starting point x . Gaston Julia (1893-1978) and Pierre Fatou (1878-1929) made a fundamental contribution to the study of iterative processes. Their contribution (Ref [3]), although regarded as a masterpiece, was largely ignored by the mathematical community until a revival in the late 1970s spawned by the discovery of fractals by Benoit Mandelbrot. For a given function f, behavior of an orbit very much depends on the selection of the starting point x . Following is a rough classification of possible behaviors: k =x p so that the sequence repeats itself Chaos k The set of points with chaotic orbits is called the Julia set for a given function f. Until quite recently the study of iterations and Julia sets has been in a prolonged limbo. B.Mandelbrot has the following to say on the development of the theory
Extractions: This article is licensed under the GNU Free Documentation License . It uses material from the Wikipedia article "List_of_mathematical_topics_(D-F)" Browse Liston listeria List of mathematical topics (D-F) litchee ... literalise Search Word: General Encyclopedia Legal Medical Computer Science Law Forum Embed a dictionary search in your own web page Link to Us Advertise Add to Favorites ...
Jean-Pierre Gueydan 44 Notes from George fatou, France, descendant of Jeanpierre Gueydan, compiledwith information from Henri Louis Gueydan and the Gueydan Harvest Times, http://www.vermilionhistorical.com/features/Biographies/jean_pierre_gueydan.htm
Extractions: By Patricia Saltzman Heard History is a collection of facts and assumptions, which paint a story so that we may better understand who we are today. The historical events concerning Jean-Pierre Gueydan and the beginning of the town of Gueydan are based on facts in an attempt to tell the fullest and most accurate story possible. Documentation is provided for the viewer. A short distance from the Mediterranean, on the southeastern coast in St. Bonnet, France, a young couple running a hotel would unknowingly contribute to American history. Pierre Gueydan and his wife, Victoire, purchased a hotel from her father, Francois Leauthier. There, they reared three children: Francois, Jean-Pierre and Clara Gertrude. Two of these children would venture across the ocean into pre-Civil War America and leave their name in a permanent location as a testament to their arrival. Francois was the first who came to the United States on March 30, 1831
Gaston M. Julia pierre fatou began his studies on mathematics in 1898 at the Ecole NormaleSupérieure in Paris. After the exams in 1901 he applied for a job at the http://www.fractalus.ch/biograf/bio_e.html
Extractions: In 1915 the Académie des Sciences published the topic of her "Grand Prix" for 1918. It should be a study regarding Iterations. The Académie des Sciences hoped for a continuation on Montel’s concept about "normale (Abbildungs-)Familien". So Fatou wrote an extensive paper covering a fundamental theory about Iterations. One assumes his intention to take part at this "Grand prix". Nobody was astonished, that other mathematicians took part, since the question had been published. So Gaston Julia developed the same theory on a very similar base. Later it was obvious that these two mathematicians worked on the very same problem going a different way. When submitting the two papers some strange things happened, it is difficult to see there the light. Seemingly Fatou did not participate at the contest, but anyway, later he was honored. It seems that Fatou did not really treat fractals, but he prepared basics for the researches of Julia and Mandelbrot. Nevertheless, Julia sets from outside the Mandelbrot set are called "Fatou Dust". My Julia-programm allows to draw such structures, but since it dyes values between maximum and minimum, these "dusts" do not appear as lots of separated spots.
Gaston M. Julia Translate this page pierre fatou begann 1898 mit dem Mathematikstudium an der Ecole Normale Supérieurein Paris und bewarb sich nach seinem Examen im Jahr 1901 für eine Stelle http://www.fractalus.ch/biograf/bio_d.html
Extractions: Fatou Julia Mandelbrot Louis Pierre Joseph Fatou 1915 gab die Académie des Sciences in Paris das Thema ihres "Grand Prix" für 1918 bekannt. Der Preis sollte für eine Studie über das Thema Iterationen verliehen werden, da sich die Académie des Sciences davon eine Weiterentwicklung von Montel's Konzept "normaler (Abbildungs-)Familien" erhoffte. Fatou schrieb 1917 einen langen Aufsatz, um die fundamentale Theorie der Iteration zu entwickeln. Obwohl man nicht sicher weiss, ob Fatou beabsichtigte, am Grand Prix teilzunehmen, vermutet man dies. Da das Thema des Grand Prix bekannt war, ist es nicht verwunderlich, dass auch andere Mathematiker dieser Zeit in diesem Themengebiet arbeiteten. So entwickelte Gaston Julia die gleiche Theorie auf eine ähnliche Art und Weise. Fatou scheint sich nicht speziell um Fraktale gekümmert zu haben, er hat vielmehr Grundlagen für die späteren Arbeiten von Julia und Mandelbrot erarbeitet. Ihm zu Ehren nennt man Julia-Figuren aus Bereichen ausserhalb der Mandelbrot-Menge "Fatou-Staub". Ich kann solche Gebilde mit meinem Julia-Programm auch erzeugen, nur zerfallen sie nicht unbedingt zu einer Vielzahl von Flecken, weil mein Programm auch Werte zwischen Maximum und Minimum einfärbt. Fatou Julia Mandelbrot Gaston Maurice Julia Es sollte eine Zeit der schlimmsten Schmerzen werden, und da vergrub er sich - wohl um sich etwas abzulenken - in ein mathematisches Problem: Es war das Verhalten der Funktion, die hinter den Julia-Figuren steckt. Nach seiner Entlassung aus dem Lazarett - der Krieg war in der Zwischenzeit beendet - veröffentlichte er ein ca. 200 Seiten starkes Buch "Mémoire sur l'iteration des fonctions rationelles".
CelebrityTrendZ: Fashion Designer - Pierre Cardin Chat Transcript fatou I ma young designer who graduated in June 2000. The press has said thatmy creations You have to contact the press service for pierre Cardin. http://www.celebritytrendz.com/fashion/designers/chat_transcripts/pierrecardin_c
Extractions: Yes, fashion journalists' opinions are very important, but I'm not influenced by the press. It's during the night, in the dark, that I'm moved to create. I am not influenced by travel, movies, etc. Nothing influences me. A creator should be copied. A creator who reminds you of someone else, that's not a creator. Souris: Hello Mr. Cardin. What's your opinion of what's happening today at Saint Laurent?
Motivate : Chaos behaviour in simple equations Gaston Julia and pierre fatou in 1918, Julia and fatou laid the foundations for what became known as fractals (a http://www.motivate.maths.org/conferences/conf3/c3_talk.shtml
Extractions: The Tent Mapping One of the great things about mathematics is that it can tell you things about the world that you could not discover in any other way. The application of mathematics to predict the way that things behave is crucial to our attempts to understand problems like how the weather changes over periods of days or of decades, how ecological balances might be affected by sudden changes in human activity, how economies will change when financial policies are altered, how to optimise the braking system of a car, how to assess risk, how turbulent air flows around an aircraft wing, or how close to Earth an approaching asteroid might pass. In all these problems we are interested in a reliable understanding of a complicated situation and an ability to predict what might happen in the future. top of page In problems like those we have listed, we are interested in arriving by some means at the correct mathematical model for the problem of interest, inputting reliable information about the past and the present state of affairs, so as to extract predictions about the future. Traditionally, mathematics had been applied to a collection of "simple" problems which described situations that are
Extractions: B. Sc. (Cum Laude) Universidad Central de Venezuela; Ph. D. University of Minnesota. Visiting Professor of Mathematics at the University of Texas at San Antonio, San Antonio, Texas 78249, USA during 1998-1999. E-mail: padron@ciens.ula.ve B. Sc. (Cum Laude) University of Miami; Ph. D. State University of New York at Stony Brook. Professor of mathematics at the University of Texas at San Antonio, Division of Mathematics, San Antonio, Texas 78249, USA. E-mail: salingar@sphere.math.utsa.edu This conversation was published electronically by RUDI Resource for Urban Design Information on March 2000. Fractals Complexity and fractal boundaries Creative freedom Universality Jungian archetypes Ecology The fractal mind Our vanishing heritage The collective mind Bibliography Fractals - Architecture - Mind - Urban Design - Complexity - Evolutionary Psychology - Ecology - Cognitive Rules Nikos Salingaros (NS) : For the past few years, I have been applying the analytic thinking of a scientist to find basic laws for architecture and urbanism, following the lead of my friend, the brilliant architectural theorist Christopher Alexander. The results derived so far show that a building, or city, is subject to the same organizational laws as a biological organism and a complex computer program. The New Architecture depends upon scientific rules rather than stylistic dictates. Using these rules, we can create new buildings that duplicate the intensely positive, nourishing feelings of the greatest historical buildings, without copying neither their form nor their style.
