Titlebook: Bifurcation without Parameters; Stefan Liebscher Book 2015 The Editor(s) (if applicable) and The Author(s), under exclusive license to Spr

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IntroductionThis chapter introduces the setting in which we shall study bifurcations without parameters. We compare it with classical bifurcation theory and give an overview and classification of the results presented in the following chapters.

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CosymmetriesCosymmetries have been introduced by Yudovich and Kurakin to study limit cycles near manifolds of equilibria via Lyapunov-Schmidt reduction [49, 50]. They turn out to be equivalent to the existence of manifolds of equilibria, provided some non-degeneracy conditions are satisfied.

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易受騙

Poincaré-Andronov-Hopf BifurcationWithout parameters, no periodic orbits bifurcate. Depending on the drift condition, two cases appear. Both are discussed in this chapter.

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https://doi.org/10.1007/978-3-319-10777-634C23,34C20,34C37,37G99,35B32; Bifurcation without parameters; Equilibria; Manifolds; Nonlinear dynamica

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