Mathematics-Dynamical Systems

Local and semi-local bifurcations in Hamiltonian dynamical systems

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Title (user) : Local and semi-local bifurcations in Hamiltonian dynamical systemsTitle (google) : Local and semi-local bifurcations in Hamiltonian dynamical systems results and examplesISBN : 9783540388944,354038894XDOI : 10.1007/3-540-38894-XGoogl...
Description

Title (user) : Local and semi-local bifurcations in Hamiltonian dynamical systems

Title (google) : Local and semi-local bifurcations in Hamiltonian dynamical systems results and examples

ISBN : 9783540388944,354038894X

DOI : 10.1007/3-540-38894-X

GoogleBook ID : -kfvAAAAMAAJ

OpenLibrary ID : OL15619262M

Edition : 1

Series : Lecture Notes in Mathematics 1893

Authors (user) : Heinz Hanβmann (auth.)

Authors (google) : Heinz Hanssmann

Publisher : Springer-Verlag Berlin Heidelberg

Language : English

Publication Date : 2007

Scanned : yes (300 DPI)

File Format : djvu

Categories : Mathematics


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Description (user) :

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.


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Description (google) :
This book demonstrates that while elliptic and hyperbolic tori determine the distribution of maximal invariant tori, they themselves form n-parameter families. Therefore, torus bifurcations of high co-dimension may be found in a single given Hamiltonian system, absent untypical conditions or external parameters. The text moves logically from the integrable case, in which symmetries allow for reduction to bifurcating equilibria, to non-integrability, where smooth parametrisations must be replaced by Cantor sets.


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Table of contents :
Front Matter....Pages I-XV
Introduction....Pages 1-15
Bifurcations of Equilibria....Pages 17-89
Bifurcations of Periodic Orbits....Pages 91-107
Bifurcations of Invariant Tori....Pages 109-142
Perturbations of Ramified Torus Bundles....Pages 143-159
Planar Singularities....Pages 161-165
Stratifications....Pages 167-171
Normal Form Theory....Pages 173-184
Proof of the Main KAM Theorem....Pages 185-200
Proofs of the Necessary Lemmata....Pages 201-206
Back Matter....Pages 207-241

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