James A. Yorke
| James Alan Yorke | |
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| Born | James Alan Yorke August 3, 1941 Plainfield, New Jersey |
| Nationality | United States |
| Fields | Math and Physics (theoretical) |
| Institutions | University of Maryland, College Park |
| Alma mater |
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| Doctoral students | Tien-Yien Li and 50 more |
| Notable awards | Japan Prize (2003) |
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 2012 he became a fellow of the American Mathematical Society.
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, 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 Sharkovsky's theorem.
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.
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