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E-raamat: Nonautonomous Bifurcation Theory: Concepts and Tools

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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.

Arvustused

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) 

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.
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