Topological Degree Approach to Bifurcation Problems

  • Michal Fečkan

Part of the Topological Fixed Point Theory and Its Applications book series (TFPT, volume 5)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Pages 1-6
  3. Back Matter
    Pages 243-261

About this book

Introduction

Topological bifurcation theory is one of the most essential topics in mathematics. This book contains original bifurcation results for the existence of oscillations and chaotic behaviour of differential equations and discrete dynamical systems under variation of involved parameters. Using topological degree theory and a perturbation approach in dynamical systems, a broad variety of nonlinear problems are studied, including: non-smooth mechanical systems with dry frictions; weakly coupled oscillators; systems with relay hysteresis; differential equations on infinite lattices of Frenkel-Kontorova and discretized Klein-Gordon types; blue sky catastrophes for reversible dynamical systems; buckling of beams; and discontinuous wave equations.

Precise and complete proofs, together with concrete applications with many stimulating and illustrating examples, make this book valuable to both the applied sciences and mathematical fields, ensuring the book should not only be of interest to mathematicians but to physicists and theoretically inclined engineers interested in bifurcation theory and its applications to dynamical systems and nonlinear analysis.

Keywords

Boundary value problem Topology Vibration calculus differential topology friction partial differential equation wave equation

Authors and affiliations

  • Michal Fečkan
    • 1
  1. 1.Department of Mathematical Analysis and Numerical Mathematics Faculty of Mathematics, Physics and InformaticsComenius UniversityBratislavaSlovakia

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4020-8724-0
  • Copyright Information Springer Netherlands 2008
  • Publisher Name Springer, Dordrecht
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4020-8723-3
  • Online ISBN 978-1-4020-8724-0
  • About this book