James Alan Yorke | |
|---|---|
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| Born | James Alan Yorke (1941-08-03)August 3, 1941 (age 84) |
| Alma mater | |
| Known for | Kaplan–Yorke conjecture |
| Awards | Japan Prize (2003) |
| Scientific career | |
| Fields | Math andPhysics (theoretical) |
| Institutions | University of Maryland, College Park |
| Doctoral students | Tien-Yien Li |
James A. Yorke (born August 3, 1941) is a Distinguished University Research Professor ofMathematics andPhysics and former chair of the Mathematics Department at theUniversity of Maryland, College Park.
 | This sectionis missing information about Yorke's career between school and his Distinguished University Professorship. Please expand the section to include this information. Further details may exist on thetalk page.(June 2025) |
Born inPlainfield, New Jersey,United States, Yorke attendedThe Pingry School, then located in Hillside, New Jersey. Yorke is now aDistinguished University Research Professor of Mathematics and Physics with the Institute for Physical Science and Technology at the University of Maryland. In June 2013, 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 andBenoit Mandelbrot were the recipients of the 2003Japan Prize in Science and Technology: Yorke was selected for his work inchaotic systems. In 2003 he was elected aFellow of the American Physical Society,[1] and in 2012 became a fellow of theAmerican Mathematical Society.[2]
He received the Doctor Honoris Causa degree from theUniversidad 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 was a 2016Thomson Reuters Citations Laureate in Physics.[5]
He and his co-authorT.Y. Li coined the mathematical termchaos in a paper they published in 1975 entitledPeriod three implies chaos,[6] in which it was proved that every one-dimensional continuous map
that has a period-3 orbit must have two properties:
(1) For each positive integerp, there is a point inR that returns to where it started afterp 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 periodp. This turned out to be a special case ofSharkovskii's theorem.[7]
The second property requires some definitions. A pair of pointsx andy 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 setS is called ascrambled set if every pair of distinct points inS is scrambled. Scrambling is a kind ofmixing.
(2) There is anuncountably infinite setS 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 ofmeasure zero (see for example the articleLogistic map), in which case the map is said to haveunobservable nonperiodicity[10]: p. 18 orunobservable chaos.
He and his colleagues (Edward Ott andCelso 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 theO.G.Y. method.
Together withKathleen T. Alligood andTim D. Sauer, he was the author of the bookChaos: An Introduction to Dynamical Systems.
