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作者 Vries, J. de (Jan), author
書名 Topological dynamical systems : an introduction to the dynamics of continuous mappings / Jan de Vries
出版項 Berlin ; Boston : De Gruyter, [2014]
國際標準書號 9783110340730 (alk. paper)
3110340739 (alk. paper)
book jacket
館藏地 索書號 處理狀態 OPAC 訊息 條碼
 數學所圖書室  QA611.5 .V754 2014    在架上    30340200538357
說明 xv, 498 pages : illustrations ; 25 cm
text rdacontent
unmediated rdamedia
volume rdacarrier
系列 De Gruyter studies in mathematics ; volume 59
De Gruyter studies in mathematics ; v. 59
附註 Includes bibliographical references (pages 481-484) and index
Introduction -- Basic notions -- Dynamical systems on the real line -- Limit behaviour -- Recurrent behaviour -- Shift systems -- Symbolic representations -- Erratic behaviour -- Topological entropy -- Topology -- The cantor set -- Hints to the exercises
This book is an introduction into the theory of discrete dynamical systems with emphasis on the topological background. It is addressed primarily to graduate students. The prerequisites for understanding this book are modest: a certain mathematical maturity and a course in General Topology are sufficient. Students who have mastered this book will have a firm basis to start research on related topics. The theory is about the behaviour of points of a Hausdorff space under the iteration of a continuous self-map. The assumption that the space is metrizable is avoided as much as possible, but where the non-metric version of the theory would become unwieldy we do not hesitate to assume metrizability. A similar remark applies to the assumption of compactness of the space. Much attention is given to dynamical systems on intervals on the real line. A wide range of topics, such as asymptotic stability, shift systems, (chain-)recurrence, topological entropy and chaos, is discussed. Every chapter concludes with a set of exercises and a section of notes, with references to the literature
主題 Topological dynamics
Topological dynamics. fast (OCoLC)fst01152680
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