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Lecture Notes in Mathematics - 1893: Local and Semi-Local Bifurcations in Hamiltonian Dynamical Systems

Results and Examples

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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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Lecture Notes in Mathematics - 1893: Local and Semi-Local Bifurcations in Hamiltonian Dynamical Systems, Heinz Hanßmann

Idioma
Publicado en
2006
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Título
Lecture Notes in Mathematics - 1893: Local and Semi-Local Bifurcations in Hamiltonian Dynamical Systems
Subtítulo
Results and Examples
Idioma
Inglés
Editorial
Springer
Publicado en
2006
Formato
Tapa blanda
Páginas
258
ISBN10
354038894X
ISBN13
9783540388944
Serie
Descripción
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.