Titlebook: Nonautonomous Bifurcation Theory; Concepts and Tools Vasso Anagnostopoulou,Christian P?tzsche,Martin Ra Book 2023 The Editor(s) (if applica

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2364-4532 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.978-3-031-29841-7978-3-031-29842-4Series ISSN 2364-4532 Series E-ISSN 2364-4931

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Frontiers in Applied Dynamical Systems: Reviews and Tutorialshttp://image.papertrans.cn/n/image/667167.jpg

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https://doi.org/10.1007/978-3-031-29842-4Bifurcation Theory; Dynamical Systems; Nonautonomous differential equations; Spectral theory; Reduction

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Introduction,amples are presented illustrating different types of nonautonomous bifurcations, which set the stage for our further analysis. Finally, we remark on topological equivalence and describe several neglected topics.

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Spectral Theory, Stability and Continuationential dichotomies, the resulting dichotomy (Sacker-Sell) spectrum and the Spectral Theorem, as well as the Lyapunov spectrum. Moreover, it is shown that hyperbolic bounded entire solutions can be continued in parameters and therefore nonhyperbolicity is necessary for bifurcation.

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Nonautonomous Bifurcation bifurcation of minimal sets. We review sufficient conditions for such bifurcations and present suitable examples. Rate-induced tipping is understood as a special case of solution bifurcation. The chapter closes with some remarks on nonautonomous Hopf bifurcations.

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Reduction Techniquesension and we describe how to obtain a Taylor approximation of integral manifolds and (2) under suitable nonresonance conditions, normal form theory yields algebraic simplification. Both approaches are based on suitable assumptions on the dichotomy spectrum.

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Nonautonomous Bifurcationand bifurcation of minimal sets and invariant graphs. In reviewing sufficient conditions for such bifurcations, we try to complement those results covered for ordinary differential equations already. A nonautonomous Sacker–Neimark bifurcation is understood as an attractor bifurcation.

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Vasso Anagnostopoulou,Christian P?tzsche,Martin RaGives a unique survey of different approaches to nonautonomous bifurcation theory.Examples guide the discussion and comparison of different approaches.Provides a unique collection of tools from the th

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