Symmetries and regular behavior of Hamiltonian systems
| Autor: | Valeriy V. Kozlov |
|---|---|
| Rok vydání: | 1996 |
| Předmět: |
Hamiltonian mechanics
Integrable system Dynamical systems theory Applied Mathematics Mathematical analysis General Physics and Astronomy Statistical and Nonlinear Physics Hamiltonian optics Hamiltonian system symbols.namesake symbols Covariant Hamiltonian field theory Superintegrable Hamiltonian system Mathematics::Symplectic Geometry Mathematical Physics Symplectic geometry Mathematics Mathematical physics |
| Zdroj: | Chaos: An Interdisciplinary Journal of Nonlinear Science. 6:1-5 |
| ISSN: | 1089-7682 1054-1500 |
| DOI: | 10.1063/1.166153 |
| Popis: | The behavior of the phase trajectories of the Hamilton equations is commonly classified as regular and chaotic. Regularity is usually related to the condition for complete integrability, i.e., a Hamiltonian system with n degrees of freedom has n independent integrals in involution. If at the same time the simultaneous integral manifolds are compact, the solutions of the Hamilton equations are quasiperiodic. In particular, the entropy of the Hamiltonian phase flow of a completely integrable system is zero. It is found that there is a broader class of Hamiltonian systems that do not show signs of chaotic behavior. These are systems that allow n commuting "Lagrangian" vector fields, i.e., the symplectic 2-form on each pair of such fields is zero. They include, in particular, Hamiltonian systems with multivalued integrals. (c) 1996 American Institute of Physics. |
| Databáze: | OpenAIRE |
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