This article is about the 20th century mathematician. There is also an 18th century clergyman James Yorke

James Yorke (clergy)

James Yorke was a British clergyman.Yorke was the son of the 1st Earl of Hardwicke and Margaret Cocks. He was Bishop of St David's from 1774 until 1779, Bishop of Gloucester from 1779 to 1781 and then Bishop of Ely from 1781 to 1808.On 29 June 1762, Yorke married Mary Maddocks, daughter of Isaac...

James A. Yorke (born August 3, 1941) is a Distinguished University Professor of Mathematics

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

 and Physics

Physics

Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

 and chair of the Mathematics Department at the University of Maryland, College Park

University of Maryland, College Park

The University of Maryland, College Park is a top-ranked public research university located in the city of College Park in Prince George's County, Maryland, just outside Washington, D.C...

. He and Benoit Mandelbrot were the recipients of the 2003 Japan Prize

Japan Prize

is awarded to people from all parts of the world whose "original and outstanding achievements in science and technology are recognized as having advanced the frontiers of knowledge and served the cause of peace and prosperity for mankind."- Explanation :...

 in Science and Technology. Yorke was selected for his work in chaotic systems.

Born in Plainfield, New Jersey

Plainfield, New Jersey

Plainfield is a city in Union County, New Jersey, United States. As of the 2010 United States Census, the city's population increased to a record high of 49,808....

, United States

United States

The United States of America is a federal constitutional republic comprising fifty states and a federal district...

, Yorke attended The Pingry School, then located in Hillside, New Jersey. 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 continuous function

F:R → R

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. (Of course this means there are infinitely many periodic points, different 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 repeated 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. Picture an egg being scrambled forever. You would expect typical atoms x and y to behave in this way. A set S is called "scrambled" if every pair of distinct points in S is scrambled. Scrambling is a kind of mixing.

(2) There is an uncountably infinite set

Uncountable set

In mathematics, an uncountable set is an infinite set that contains too many elements to be countable. The uncountability of a set is closely related to its cardinal number: a set is uncountable if its cardinal number is larger than that of the set of all natural numbers.-Characterizations:There...

S that is scrambled.

A map satisfying property 2 is sometimes called "chaotic in the sense of Li and Yorke".

Yorke is known for his jovial character and frequently dresses like Santa Clause at department holiday parties.

External links

• Website at the University of Maryland