{"title":"Anatole Katok","description":null,"products":[{"product_id":"introduction-to-the-modern-theory-of-dynamical-systems-book-anatole-katok-9780521575577","title":"Introduction to the Modern Theory of Dynamical Systems","description":"This book provided the first self-contained comprehensive exposition of the theory of dynamical systems as a core mathematical discipline closely intertwined with most of the main areas of mathematics. The authors introduce and rigorously develop the theory while providing researchers interested in applications with fundamental tools and paradigms. The book begins with a discussion of several elementary but fundamental examples. These are used to formulate a program for the general study of asymptotic properties and to introduce the principal theoretical concepts and methods.  The main theme of the second part of the book is the interplay between local analysis near individual  orbits and the global complexity of the orbit structure. The third and fourth parts develop the theories of  low-dimensional dynamical systems and hyperbolic dynamical systems in depth. Over 400 systematic exercises are included in the text. The book is aimed at students and researchers in mathematics at all levels from advanced undergraduate up.","brand":"WoB","offers":[{"title":"US \/ WELL_READ \/ SBYB","offer_id":50354396954897,"sku":"CIN0521575575A","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":50474938925329,"sku":"GOR010614908","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ NEW \/ INGRAM","offer_id":51003154530577,"sku":"NIN9780521575577","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52481816723729,"sku":"NLS9780521575577","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0521575575.jpg?v=1750697954"},{"product_id":"lectures-on-surfaces-book-anatole-katok-9780821846797","title":"Lectures on Surfaces","description":"Surfaces are among the most common and easily visualized mathematical objects, and their study brings into focus fundamental ideas, concepts, and methods from geometry, topology, complex analysis, Morse theory, and group theory. At the same time, many of those notions appear in a technically simpler and more graphic form than in their general 'natural' settings. The first, primarily expository, chapter introduces many of the principal actors - the round sphere, flat torus, Mobius strip, Klein bottle, elliptic plane, etc. - as well as various methods of describing surfaces, beginning with the traditional representation by equations in three-dimensional space, proceeding to parametric representation, and also introducing the less intuitive, but central for our purposes, representation as factor spaces.It concludes with a preliminary discussion of the metric geometry of surfaces, and the associated isometry groups. Subsequent chapters introduce fundamental mathematical structures - topological, combinatorial (piecewise linear), smooth, Riemannian (metric), and complex - in the specific context of surfaces. The focal point of the book is the Euler characteristic, which appears in many different guises and ties together concepts from combinatorics, algebraic topology, Morse theory, ordinary differential equations, and Riemannian geometry.The repeated appearance of the Euler characteristic provides both a unifying theme and a powerful illustration of the notion of an invariant in all those theories. The assumed background is the standard calculus sequence, some linear algebra, and rudiments of ODE and real analysis. All notions are introduced and discussed, and virtually all results proved, based on this background. This book is a result of the MASS course in geometry in the fall semester of 2007.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51463447544081,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ VERY_GOOD \/ SBYB","offer_id":51463448068369,"sku":"CIN0821846795VG","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0821846795.jpg?v=1763118108"},{"product_id":"introduction-to-the-modern-theory-of-dynamical-systems-book-anatole-katok-9780521341875","title":"Introduction to the Modern Theory of Dynamical Systems","description":"This book provided the first self-contained comprehensive exposition of the theory of dynamical systems as a core mathematical discipline closely intertwined with most of the main areas of mathematics. The authors introduce and rigorously develop the theory while providing researchers interested in applications with fundamental tools and paradigms. The book begins with a discussion of several elementary but fundamental examples. These are used to formulate a program for the general study of asymptotic properties and to introduce the principal theoretical concepts and methods.  The main theme of the second part of the book is the interplay between local analysis near individual  orbits and the global complexity of the orbit structure. The third and fourth parts develop the theories of  low-dimensional dynamical systems and hyperbolic dynamical systems in depth. Over 400 systematic exercises are included in the text. The book is aimed at students and researchers in mathematics at all levels from advanced undergraduate up.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52400879862033,"sku":"NLS9780521341875","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":53130938450193,"sku":"GOR014761022","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ NEW \/ INGRAM","offer_id":53185997963537,"sku":"NIN9780521341875","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9780521341875.jpg?v=1758752932"},{"product_id":"rigidity-in-higher-rank-abelian-group-actions-volume-1-introduction-and-cocycle-book-anatole-katok-9780521879095","title":"Rigidity in Higher Rank Abelian Group Actions: Volume 1, Introduction and Cocycle Problem","description":"This self-contained monograph presents rigidity theory for a large class of dynamical systems, differentiable higher rank hyperbolic and partially hyperbolic actions. This first volume describes the subject in detail and develops the principal methods presently used in various aspects of the rigidity theory. Part I serves as an exposition and preparation, including a large collection of examples that are difficult to find in the existing literature. Part II focuses on cocycle rigidity, which serves as a model for rigidity phenomena as well as a useful tool for studying them. The book is an ideal reference for applied mathematicians and scientists working in dynamical systems and a useful introduction for graduate students interested in entering the field. Its wealth of examples also makes it excellent supplementary reading for any introductory course in dynamical systems.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52682847289617,"sku":"NLS9780521879095","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9780521879095.jpg?v=1762319157"}],"url":"https:\/\/www.worldofbooks.com\/en-gb\/collections\/author-books-by-anatole-katok.oembed","provider":"World of Books ","version":"1.0","type":"link"}