James A. Yorke

James A. Yorke

James A. Yorke (born August 3, 1941) is a Distinguished University Professor of Mathematics and Physics and chair of the Mathematics Department at the University of Maryland, College Park. He is also a recipient of the 2003 Japan Prize for his work in chaotic systems.

Born in Plainfield, New Jersey, United States, 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 1-dimensional map

:"R" → "R"

that contains 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 S that is scrambled.

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

References

*T.Y. Li, and J.A. Yorke, "Period Three Implies Chaos", American Mathematical Monthly 82, 985 (1975).

* [http://yorke.umd.edu/ Website at the University of Maryland]

Wikimedia Foundation. 2010.

Look at other dictionaries:

• James Yorke — James Yorke, 2011 James A. Yorke (* 3. August 1941 in Plainfield, New Jersey, USA) ist ein US amerikanischer Professor für Physik und Mathematik und Vorsitzender des Mathematik Departments der University of Maryland, College Park. Yorke ging zur… …   Deutsch Wikipedia

• James Yorke — may refer to:* James A. Yorke, mathematician * James Yorke (clergy) …   Wikipedia

• Yorke (homonymie) — Yorke Cette page d’homonymie répertorie les différents sujets et articles partageant un même nom. Yorke peut désigner: Lieux Péninsule de Yorke en Australie Personnes Charles Philip Yorke, un homme politique anglais du XIXe siècle Charles Yorke,… …   Wikipédia en Français

• James York — may refer to:*James W. York (1939 )American mathematical physicist, expert on general relativity *James Warren York (1839 1927), American musician and business figure *James Harlan York (1947 ), American baseball playerSee also: *James A. Yorke… …   Wikipedia

• Yorke — Cette page d’homonymie répertorie les différents sujets et articles partageant un même nom. Yorke peut désigner : Lieux Péninsule de Yorke en Australie Personnes Charles Philip Yorke, un homme politique anglais du XIXe siècle Charles Yorke,… …   Wikipédia en Français

• James Yorke (clergy) — James Yorke (9 March 1730 ndash; 26 August 1808) was a British clergyman.Yorke was the son of the 1st Earl of Hardwicke and Margaret Cocks. He was Bishop of Gloucester from 1779 to 1781 and then Bishop of Ely from 1781 to 1808. On 29 June 1762,… …   Wikipedia

• James Lavelle — (* 1974 in Oxford, Vereinigtes Königreich) ist ein englischer DJ, Produzent und Veranstalter. Er ist Gründer und Eigentümer des Musiklabels Mo Wax. Inhaltsverzeichnis 1 Leben und Werk 2 UNKLE 2.1 Lavelle mit DJ Shadow …   Deutsch Wikipedia

• Yorke — ist der Familienname folgender Personen: Billy Yorke, britische Tennisspielerin Dwight Yorke (* 1971), Fußballspieler aus Trinidad und Tobago James Yorke (* 1941), US amerikanischer Physiker Margaret Yorke (* 1930), britische Romanautorin Thom… …   Deutsch Wikipedia

• James Yorke Scarlett — Sir James Yorke Scarlett GCB (* 1. Februar 1799; † 6. Dezember 1871) war ein britischer General und Teilnehmer des Krimkrieges. Leben Scarlett wurde als zweiter Sohn …   Deutsch Wikipedia

• James Langhorne — James Archibald Dunboyne Langhorne (born 24th February 1879 and died at St John s Wood, London, England on the 11th May 1950) was a Brigadier in the British Army.He was the son of Reverend John Langhorne and Frances Yorke.He was educated at… …   Wikipedia