Handbook of Topological Fixed Point Theory

Robert F. Brown, Massimo Furi, L. Gorniewicz, Boju Jiang1402032218, 9781402032219, 9781402032226, 1402032226

This book is the first in the world literature presenting all new trends in topological fixed point theory. Until now all books connected to the topological fixed point theory were devoted only to some parts of this theory. This book will be especially useful for post-graduate students and researchers interested in the fixed point theory, particularly in topological methods in nonlinear analysis, differential equations and dynamical systems. The content is also likely to stimulate the interest of mathematical economists, population dynamics experts as well as theoretical physicists exploring the topological dynamics.

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Table of contents :
front-matter……Page 1
1Coincidence Theory……Page 10
2On the Lefschetz Fixed Point Theorem……Page 50
3Linearizations for Maps of Nilmanifolds and Solvmanifolds……Page 90
4Homotopy Minimal Periods……Page 135
5Periodic Points and Braid Theory……Page 177
6Fixed Point Theory of Multivalued Weighted Maps……Page 223
7Fixed Point Theory for Homogeneous Spaces A Brief Survey……Page 270
8A Note on Equivariant Fixed Point Theory……Page 290
9Equivariant Degree……Page 304
10Bifurcations of Solutions of SO(2)-Symmetric Nonlinear Problems with Variational Structure……Page 341
11Nielsen Root Theory……Page 376
12More about Nielsen Theories and Their Applications……Page 433
13Algebraic Techniques for Calculating the Nielsen Number on Hyperbolic Surfaces……Page 463
14Fibre Techniques in Nielsen Theory Calculations……Page 488
15Wecken Theorem for Fixed and Periodic Points……Page 554
16A Primer of Nielsen Fixed Point Theory……Page 615
17Nielsen Fixed Point Theory on Surfaces……Page 644
18Relative Nielsen Theory……Page 656
19Applicable Fixed Point Principles……Page 683
20The Fixed Point Index of the Poincaré Translation Operator on Differentiable Manifolds……Page 736
21On the Existence of Equilibria and Fixed Points of Maps under Constraints……Page 778
22Topological Fixed Point Theory and Nonlinear Differential Equations……Page 862
23Fixed Point Results Based on the Ważewski Method……Page 900
back-matter……Page 939