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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
- Taal
- Jaar van publicatie
- 2006
- product-detail.submit-box.info.binding
- (Paperback)
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- Titel
- Lecture Notes in Mathematics - 1893: Local and Semi-Local Bifurcations in Hamiltonian Dynamical Systems
- Ondertitel
- Results and Examples
- Taal
- Engels
- Auteurs
- Heinz Hanßmann
- Uitgever
- Springer
- Jaar van publicatie
- 2006
- Formaat
- Paperback
- Aantal pagina's
- 258
- ISBN10
- 354038894X
- ISBN13
- 9783540388944
- Reeks
- Tags
- Non-fictie, Wetenschap en Wiskunde, Natuurwetenschappen, Wetenschap, Wiskunde, Fysica, West-Europa, Theoretische Fysica, Wiskundige Analyse, Bewijsvoering
- Aantekening
- 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.