«Science History»
Yoccoz, Jean-Christophe

Jean-Christophe Yoccoz


Born: 29 May 1957 in Paris, France
Died: 3 September 2016


Jean-Christophe Yoccoz was placed first in the entrance examination for the École Normale Supérieure and also for the École Polytechnique in 1975. He received the Agrégation de Mathématiques in 1977 in joint first position.

Yoccoz did his military service in Brazil in 1981-1983. He was a student of M Herman and submitted his doctoral thesis in 1985. As a student of Herman, a leading word expert on dynamical systems, it was not surprising that Yoccoz would himself work on dynamical systems. However, it was remarkable how quickly Yoccoz was to establish himself as the most brilliant researcher in this area. In his thesis, Yoccoz improved theorems of his supervisor Herman by giving simpler proofs but also obtaining the same results under weaker hypotheses.

Given his outstanding work it was clear that he would quickly be offered appointments and indeed he was appointed as professor at the University of Paris-Sud (Orsay). He became a member of the Institut Universitaire de France and a member of the Unité Recherche Associé "Topology and Dynamics" of the Centre National de la Recherche Scientifique at Orsay.

At the International Congress of Mathematicians in Zürich in 1994, Yoccoz received his greatest honour for this work on dynamical systems when he was awarded a Fields Medal. In his own address to the Congress, he began by stating the aim of his subject:-

Broadly speaking, the goal of the theory of dynamical systems is, as it should be, to understand most of the dynamics of most systems.
The theory of dynamical systems really began with Poincaré who was studying the stability of the solar system. This is typical of what the theory of a dynamical system tries to do: it describes how a system evolves over time given a rule which, for any particular state of the system, describes the following state. The solar system example shows exactly what one wants to know - given any configuration of the system it evolves according to Newton's laws but will it remain stable or, after many years, will one of the planets be ejected from the system?

After Poincaré, the theory was developed by a large number of mathematicians such as Arnold, Fatou, Herman, Julia, Kolmogorov, Palis, Siegel, Smale and Yoccoz. Douady writes in [3]:-

... they have proved stability properties - dynamic stability, such as that sought for the solar system, or structural stability, meaning persistence under parameter changes of the global properties of the system.
Yoccoz in his own address at the International Congress of Mathematicians in Zürich in 1994 said:-
The dynamical features that we are able to understand fall into two classes, hyperbolic dynamics and quasiperiodic dynamics; it my well happen, especially in the conservative case, that a system exhibits both hyperbolic and quasiperiodic features. ... we seek to extend these concepts, keeping a reasonable understanding of the dynamics, in order to account for as many systems as we can. The big question is then: Are these concepts sufficient to understand most systems?
Douady describes Yoccoz's contributions in general terms in [2] but in more detail in [3] which was the article describing the mathematics leading to the award of the Fields Medal. We quote [2] and advise those looking for more technicalities to consult [3]:-
He combines an extremely acute geometric intuition, an impressive command of analysis, and a penetrating combinatorial sense to play the chess game at which he excels. He occasionally spends half a day on mathematical "experiments", by hand or by computer. "When I make such an experiment", he says, "it is not just the results that interest me, but the manner in which it unfolds, which sheds light on what is really going on." Yoccoz has developed a method of combinatorial study of Julia sets and Mandelbrot sets - called "Yoccoz puzzles" - which permit deep insight.

Article by: J J O'Connor and E F Robertson

April 1998
MacTutor History of Mathematics
[http://www-history.mcs.st-andrews.ac.uk/Biographies/Yoccoz.html]
Search All Ebay* AU* AT* BE* CA* FR* DE* IN* IE* IT* MY* NL* PL* SG* ES* CH* UK*
Blue Book of Gun Values 2018 2019 39th Edition

$99.00
End Date: Friday Sep-14-2018 2:23:27 PDT
Buy It Now for only: $99.00
|
Human Anatomy by McKinley, 5th Ed. Instructor's Review Copy, U.S. Version

$147.35
End Date: Saturday Aug-25-2018 7:32:39 PDT
Buy It Now for only: $147.35
|
Complete Mystical Records of Dr. John Dee by Kevin Klein Hardcover Book Free Shi

$69.98
End Date: Monday Sep-10-2018 18:59:09 PDT
Buy It Now for only: $69.98
|
ELVIRA Mistress of the Dark hardcover book Cassandra Peterson SEALED NEW COPY

$19.75
End Date: Sunday Sep-9-2018 23:26:47 PDT
Buy It Now for only: $19.75
|
Marc Davis : Walt Disney's Renaissance Man NEW HC/DJ DISNEY Editions

$15.98
End Date: Tuesday Aug-28-2018 5:21:11 PDT
Buy It Now for only: $15.98
|
Astrophysics for People in a Hurry by Neil deGrasse Tyson (Physics) [Hardcover]

$9.53
End Date: Monday Sep-3-2018 19:43:15 PDT
Buy It Now for only: $9.53
|
No-Drama Discipline : The Whole-Brain Way to Calm the Chaos and Nurture Your...

$18.75
End Date: Thursday Sep-13-2018 9:15:03 PDT
Buy It Now for only: $18.75
|
Unhinged: An Insider's Account of the Trump White House

$85.00
End Date: Friday Sep-14-2018 6:51:49 PDT
Buy It Now for only: $85.00
|

You can claim your cashback, from Samsung, using the online form.

Start: 08 Jun 2017 | End: 30 Apr 2018

The Smarter Way, Delivered - Try Dollar Shave Club!

Start: 03 Nov 2017 | End: 03 Nov 2018

High-speed, premium and wireless Internet access, Oversized work desk in every guestroom, Full-service Business Centers, 24-hour room service, Fitness Centers and Spas, Chic public spaces for entertaining or relaxing, Concierge services

Start: 28 Mar 2017 | End: 28 Feb 2018

Search All Amazon* UK* DE* FR* JP* CA* CN* IT* ES* IN* BR* MX
Booking.com B.V. is based in Amsterdam in the Netherlands. Ready for some statistics? Our 1,534,024 properties, including 860,482 holiday rentals, are located in 123,105 destinations in 229 countries and territories, and are supported internationally by 198 offices in 70 countries.
2013 Copyright © Techhap.com Mobile version 2015 | PeterLife & company
Skimlinks helps publishers monetize editorial content through automated affiliate links for products. Affiliate programm.
Terms of use Link at is mandatory if site materials are using fully or particulary.
Were treated to the site administrator, a cup of coffee *https://paypal.me/peterlife
Yandex.ru