The Kolmogorov legacy in physics: a century of turbulence and complexity

the Present Volume, Published At The Occasion Of His 100th Birthday Anniversary, Is A Collection Of Articles That Reviews The Impact Of Kolomogorov's Work In The Physical Sciences And Provides An Introduction To The Modern Developments That Have Been Triggered In This Way To Encompass Recent Applications In Biology, Chemistry, Information Sciences And Finance. This Book Addresses Scientists And Postgraduate Students In Applied Mathematics And Theoretical Physics. Andre N. Kolmogorov (1903-1987) est sans doute l'un des plus grands scientifiques du XXe sicle. Surtout connu comme mathmaticien, il n'en a pas moins obtenu des rsultats de tout premier ordre en physique. Comme le raconte dans cet ouvrage son ancien lve et collaborateur Yakov G. Sinai, on oubliait facilement son gnie mathmatique, tant il aimait discuter des derniers rsultats exprimentaux en physique, mais aussi de musique ou de posie. l'occasion du centenaire de sa naissance, une vingtaine de physiciens de renom lui rendent hommage en revisitant son poustouflant hritage scientifique dans quatre domaines de la physique : le chaos et les systmes dynamiques, la complexit algorithmique et la thorie de l'information, la turbulence, et enfin les applications de la thorie des probabilits la renormalisation et la finance. Destin aux tudiants des 2e et 3e cycles comme aux chercheurs, cet ouvrage propose un tour d'horizon des travaux de Kolmogorov dans ces domaines, et analyse l'volution jusqu' nos jours des thories sous-jacentes et de leurs dveloppements les plus rcents en informatique, biologie, chimie et finance. The present volume, published at the occasion of his 100th birthday anniversary, is a collection of articles that reviews the impact of Kolomogorov's work in the physical sciences and provides an introduction to the modern developments that have been triggered in this way to encompass recent applications in biology, chemistry, information sciences and finance. This book addresses scientists and postgraduate students in applied mathematics and theoretical physics. TOC:Part I: Chaos and Dynamical Systems.-Part II: Algorithmic Complexity and Information Theory.-Part III: Turbulence.-Part IV: Applications of Probability Theory At the end of the 19th century H. Poincaré rigorously showed that a generic Hamiltonian system with few degrees of freedom described by Newton's equations is not integrable [1]. TheKolmogorov Legacy in Physics Kolmogorov Pathways from Integrabilityto Chaos and Beyond 18 1 A General Perspective 18 2 Two Degrees of Freedom: Chirikov’s Standard Map 22 1 A General Perspective......Page 18 2 Two Degrees of Freedom: Chirikov’s Standard Map......Page 22