Overview
- Comprehensive theory of chaos in nonlinear dynamical systems with applications to mechanics and vibrations
- Precise and complete proofs of derived results
- Many stimulating and illustrative examples
- Rigorous proof on the existence of chaos for stick-slip systems
- Extension of Smale horseshoe to inflated dynamical systems
Part of the book series: Nonlinear Physical Science (NPS)
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Table of contents (7 chapters)
Keywords
About this book
"Bifurcation and Chaos in Discontinuous and Continuous Systems" provides rigorous mathematical functional-analytical tools for handling chaotic bifurcations along with precise and complete proofs together with concrete applications presented by many stimulating and illustrating examples. A broad variety of nonlinear problems are studied involving difference equations, ordinary and partial differential equations, differential equations with impulses, piecewise smooth differential equations, differential and difference inclusions, and differential equations on infinite lattices as well.
This book is intended for mathematicians, physicists, theoretically inclined engineers and postgraduate students either studying oscillations of nonlinear mechanical systems or investigating vibrations of strings and beams, and electrical circuits by applying the modern theory of bifurcation methods in dynamical systems.
Dr. Michal Fečkan is a Professor at the Department of Mathematical Analysis and Numerical Mathematics on the Faculty of Mathematics, Physics and Informatics at the Comenius University in Bratislava, Slovakia. He is working on nonlinear functional analysis, bifurcation theory and dynamical systems with applications to mechanics and vibrations.
Reviews
From the reviews:
“The purpose of this monograph … is to present a ‘comprehensive bifurcation theory of chaos in nonlinear dynamical systems with applications to mechanics and vibrations’. … Each chapter concludes with a list of references; a detailed index can be found at the end of the book. The monograph will attract the interest of researchers working with continuous and discontinuous dynamical systems and in related areas, as well as specialists interested in applied problems where nonlinear oscillations, bifurcations, and chaos occur.” (Yuri V. Rogovchenko, Zentralblatt MATH, Vol. 1234, 2012)
Authors and Affiliations
Bibliographic Information
Book Title: Bifurcation and Chaos in Discontinuous and Continuous Systems
Authors: Michal Fečkan
Series Title: Nonlinear Physical Science
DOI: https://doi.org/10.1007/978-3-642-18269-3
Publisher: Springer Berlin, Heidelberg
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2011
eBook ISBN: 978-3-642-18269-3Published: 30 May 2011
Series ISSN: 1867-8440
Series E-ISSN: 1867-8459
Edition Number: 1
Number of Pages: XII, 378
Additional Information: Jointly published with Higher Education Press
Topics: Theoretical, Mathematical and Computational Physics, Classical Mechanics, Dynamical Systems and Ergodic Theory, Vibration, Dynamical Systems, Control, Analysis