Homotopy Methods in Topological Fixed and Periodic Points Theory (Topological Fixed Point Theory and Its Applications, 3) - Hardcover

Jezierski, Jerzy; Marzantowicz, Waclaw

Hardcover

ISBN 10: 1402039301 ISBN 13: 9781402039300

Publisher: Springer, 2005

Synopsis

The notion of a ?xed point plays a crucial role in numerous branches of mat- maticsand its applications. Informationabout the existence of such pointsis often the crucial argument in solving a problem. In particular, topological methods of ?xed point theory have been an increasing focus of interest over the last century. These topological methods of ?xed point theory are divided, roughly speaking, into two types. The ?rst type includes such as the Banach Contraction Principle where the assumptions on the space can be very mild but a small change of the map can remove the ?xed point. The second type, on the other hand, such as the Brouwer and Lefschetz Fixed Point Theorems, give the existence of a ?xed point not only for a given map but also for any its deformations. This book is an exposition of a part of the topological ?xed and periodic point theory, of this second type, based on the notions of Lefschetz and Nielsen numbers. Since both notions are homotopyinvariants, the deformationis used as an essential method, and the assertions of theorems typically state the existence of ?xed or periodic points for every map of the whole homotopy class, we refer to them as homotopy methods of the topological ?xed and periodic point theory.

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Reviews

写像の周期点理論におけるホモトピー法について体系的に解説した最初のテキストブックである.大学院生や研究者を対象に、位相空間における古典的な不動点理論の基本的概念やレフシェッツ・ホップ・ウェケンの不動点定理の新しい証明法などが扱われている.周期点理論が、連続写像のLefschetz数やNielsen数に関連したNielsen-Jiang周期数の応用を通して明らかにされており、ウェケンの周期点定理については、本書の後半で論述されている.また、ホモトピーの最小周期問題に関するいくつかの結果が、Aarkovsky定理、ダイナミックな同変写像や位相的なエントロピーとの関連への応用の中で解明されている.位相空間における不動点理論や周期点理論のホモトピー法の問題と最新の研究成果について詳述したハイレベルの研究文献でもある.位相空間の不動点理論や応用、力学系、位相幾何学分野の研究者や大学院生の方々に、広くお薦めする.
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Edition details

• Publisher: Springer
• Publication date: 2005
• Language: English
• ISBN 10: 1402039301
• ISBN 13: 9781402039300
• Binding: Hardcover
• Number of pages: 332