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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
- Lingua
- Pubblicato
- 2006
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- (In brossura)
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- Titolo
- Lecture Notes in Mathematics - 1893: Local and Semi-Local Bifurcations in Hamiltonian Dynamical Systems
- Sottotitolo
- Results and Examples
- Lingua
- Inglese
- Autori
- Heinz Hanßmann
- Editore
- Springer
- Pubblicato
- 2006
- Formato
- In brossura
- Pagine
- 258
- ISBN10
- 354038894X
- ISBN13
- 9783540388944
- Serie
- Tag
- Saggistica, Scienza e Matematica, Scienze Naturali, Scienza, Matematica, Fisica, Europa Occidentale, Fisica Teorica, Analisi matematica, Prova
- Descrizione
- 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.