Local and Semi-Local Bifurcations in Hamiltonian Dynamical Systems

出版者:Springer Verlag

作者:Hanbmann, Heinz

页数:237

价格:$ 79.04

装帧:Pap

isbn号码:9783540388944

丛书系列:Lecture Notes in Mathematics

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Once again KAM theory is committed in the context of nearly integrable Hamiltonian systems. While elliptic and hyperbolic tori determine the distribution of maximal invariant tori, they themselves form n-parameter families. Hence, without the need for untypical conditions or external parameters, torus bifurcations of high co-dimension may be found in a single given Hamiltonian system. The text moves gradually from the integrable case, in which symmetries allow for reduction to bifurcating equilibria, to non-integrability, where smooth parametrisations have to be replaced by Cantor sets. Planar singularities and their versal unfoldings are an important ingredient that helps to explain the underlying dynamics in a transparent way.