Homotopy Methods in Topological Fixed and Periodic Points Theory

2006. Auflage 2005
ISBN: 978-1-4020-3930-0
Verlag: Springer

Buch, Englisch, 320 Seiten, Format (B × H): 167 mm x 248 mm, Gewicht: 1420 g

Reihe: Topological Fixed Point Theory and Its Applications

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.

Zielgruppe

Research

Autoren/Hrsg.

Jezierski, Jerzy

Marzantowicz, Waclaw

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Mathematik | Informatik Mathematik Topologie Mengentheoretische Topologie
• Mathematik | Informatik Mathematik Topologie Algebraische Topologie

Inhaltsverzeichnis

Fixed Point Problems.- Lefschetz-Hopf Fixed Point Theory.- Periodic Points by the Lefschetz Theory.- Nielsen Fixed Point Theory.- Periodic Points by the Nielsen Theory.- Homotopy Minimal Periods.- Related Topics and Applications.