To install click the Add extension button. That's it.

The source code for the WIKI 2 extension is being checked by specialists of the Mozilla Foundation, Google, and Apple. You could also do it yourself at any point in time.

Kelly Slayton
Congratulations on this excellent venture… what a great idea!
Alexander Grigorievskiy
I use WIKI 2 every day and almost forgot how the original Wikipedia looks like.
Live Statistics
English Articles
Improved in 24 Hours
Added in 24 Hours
What we do. Every page goes through several hundred of perfecting techniques; in live mode. Quite the same Wikipedia. Just better.

James A. Yorke

From Wikipedia, the free encyclopedia

James Alan Yorke
James Alan Yorke

(1941-08-03) August 3, 1941 (age 82)
Alma mater
Known forKaplan–Yorke conjecture
AwardsJapan Prize (2003)
Scientific career
FieldsMath and Physics (theoretical)
InstitutionsUniversity of Maryland, College Park
Doctoral studentsTien-Yien Li

James A. Yorke (born August 3, 1941) is a Distinguished University Research Professor of Mathematics and Physics and former chair of the Mathematics Department at the University of Maryland, College Park.

Born in Plainfield, New Jersey, United States, Yorke attended The Pingry School, then located in Hillside, New Jersey. Yorke is now a Distinguished University Research Professor of Mathematics and Physics with the Institute for Physical Science and Technology at the University of Maryland. In June 2013, Dr. Yorke retired as chair of the University of Maryland's Math department. He devotes his university efforts to collaborative research in chaos theory and genomics.

He and Benoit Mandelbrot were the recipients of the 2003 Japan Prize in Science and Technology: Yorke was selected for his work in chaotic systems. In 2003 He was elected a Fellow of the American Physical Society.[1] and in 2012 became a fellow of the American Mathematical Society.[2]

He received the Doctor Honoris Causa degree from the Universidad Rey Juan Carlos, Madrid, Spain, in January 2014.[3] In June 2014, he received the Doctor Honoris Causa degree from Le Havre University, Le Havre, France.[4] He received the Thomson Reuters Citations Laureate in Physics 2016.[5]

YouTube Encyclopedic

  • 1/3
    6 498 011
    307 264
    1 592 534
  • The unexpected math behind Van Gogh's "Starry Night" - Natalya St. Clair
  • 21. Chaos and Reductionism
  • Flat Earth Theory - Ultra Spiritual Life episode 39



Period three implies chaos

He and his co-author T.Y. Li coined the mathematical term chaos in a paper they published in 1975 entitled Period three implies chaos,[6] in which it was proved that any one-dimensional continuous map


that has a period-3 orbit must have two properties:

(1) For each positive integer p, there is a point in R that returns to where it started after p applications of the map and not before.

This means there are infinitely many periodic points (any of which may or may not be stable): different sets of points for each period p. This turned out to be a special case of Sharkovskii's theorem.[7]

The second property requires some definitions. A pair of points x and y is called “scrambled” if as the map is applied repeatedly to the pair, they get closer together and later move apart and then get closer together and move apart, etc., so that they get arbitrarily close together without staying close together. The analogy is to an egg being scrambled forever, or to typical pairs of atoms behaving in this way. A set S is called a scrambled set if every pair of distinct points in S is scrambled. Scrambling is a kind of mixing.

(2) There is an uncountably infinite set S that is scrambled.

A map satisfying Property 2 is sometimes called "chaotic in the sense of Li and Yorke".[8][9] Property 2 is often stated succinctly as their article's title phrase "Period three implies chaos". The uncountable set of chaotic points may, however, be of measure zero (see for example the article Logistic map), in which case the map is said to have unobservable nonperiodicity[10]: p. 18  or unobservable chaos.

O.G.Y control method

He and his colleagues (Edward Ott and Celso Grebogi) had shown with a numerical example that one can convert a chaotic motion into a periodic one by a proper time-dependent perturbation of the parameter. This article is considered a classic among the works in the control theory of chaos, and their control method is known as the O.G.Y. method.


Together with Kathleen T. Alligood and Tim D. Sauer, he was the author of the book Chaos: An Introduction to Dynamical Systems.


  1. ^ "APS Fellow Archive". APS. Retrieved 17 September 2020.
  2. ^ List of Fellows of the American Mathematical Society, retrieved 2013-09-01
  3. ^ Doctor Honoris Causa degree from the Universidad Rey Juan Carlos, Madrid, Spain, archived from the original on 2018-06-15, retrieved 2017-07-25
  4. ^ Doctor Honoris Causa degree from Le Havre University, Le Havre, France
  5. ^ Thomson Reuters Citations Laureate in Physics
  6. ^ T.Y. Li, and J.A. Yorke, Period Three Implies Chaos, American Mathematical Monthly 82, 985 (1975).
  7. ^ Sharkovskii, A. N. (1964). "Co-existence of cycles of a continuous mapping of the line into itself". Ukrainian Math. J. 16: 61–71.
  8. ^ Blanchard, F.; Glasner, E.; Kolyada, S.; Maass, A. (2002). "On Li–Yorke pairs". Journal für die reine und angewandte Mathematik. 547: 51–68.
  9. ^ Akin, E.; Kolyada, S. (2003). "Li–Yorke sensitivity". Nonlinearity. 16 (4): 1421–1433. Bibcode:2003Nonli..16.1421A. doi:10.1088/0951-7715/16/4/313. S2CID 250751553.
  10. ^ Collet, Pierre; Eckmann, Jean-Pierre (1980). Iterated Maps on the Interval as Dynamical Systems. Birkhäuser. ISBN 3-7643-3510-6.

External links

This page was last edited on 2 May 2024, at 13:13
Basis of this page is in Wikipedia. Text is available under the CC BY-SA 3.0 Unported License. Non-text media are available under their specified licenses. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc. WIKI 2 is an independent company and has no affiliation with Wikimedia Foundation.