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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
- Language
- Released
- 2006
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- Title
- Lecture Notes in Mathematics - 1893: Local and Semi-Local Bifurcations in Hamiltonian Dynamical Systems
- Subtitle
- Results and Examples
- Language
- English
- Authors
- Heinz Hanßmann
- Publisher
- Springer
- Released
- 2006
- Format
- Paperback
- Pages
- 258
- ISBN10
- 354038894X
- ISBN13
- 9783540388944
- Series
- Tags
- Non-Fiction, Science & Math, Natural sciences, Science, Mathematics, Physics, Western Europe, Theoretical Physics, Mathematical Analysis, Proof
- Description
- 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.