Nonautonomous Bifurcation Theory - Concepts and Tools

Bifurcation theory is a major topic in dynamical systems theory with profound applications. However, in contrast to autonomous dynamical systems, it is not clear what a bifurcation of a nonautonomous dynamical system actually is, and so far, various different approaches to describe qualitative changes have been suggested in the literature. The aim of this book is to provide a concise survey of the area and equip the reader with suitable tools to tackle nonautonomous problems. A review, discussion and comparison of several concepts of bifurcation is provided, and these are formulated in a unified notation and illustrated by means of comprehensible examples. Additionally, certain relevant tools needed in a corresponding analysis are presented.

List of contents

Introduction.- Part I Nonautonomous differential equations - Spectral theory, stability and continuation.- Nonautonomous bifurcation.- Reduction techniques.- Part II Nonautonomous difference equations - Spectral theory, stability and continuation.- Nonautonomous bifurcation.- Reduction techniques.

Report

The authors aim at a survey where recent main developments and results are discussed, with many references to the literature for more concrete examples, details and proofs. This text offers a start to the field with many pointers to literature. (Hil G. E. Meijer, Mathematical Reviews, January, 2025) 

Product details

• Authors: Vasso Anagnostopoulou, Christian Pötzsche, Rasmuss, Martin Rasmussen
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 10.07.2023
• EAN: 9783031298417
• ISBN: 978-3-0-3129841-7
• No. of pages: 156
• Dimensions: 155 mm x 9 mm x 235 mm
• Illustrations: X, 156 p. 1 illus.
• Series: Frontiers in Applied Dynamical Systems: Reviews and Tutorials
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Analysis