An asymptotic method for constructing the Poincaré mapping in describing the transition of dynamical chaos in Hamiltonian systems. (Q1417745)
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scientific article; zbMATH DE number 2021802
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An asymptotic method for constructing the Poincaré mapping in describing the transition of dynamical chaos in Hamiltonian systems. |
scientific article; zbMATH DE number 2021802 |
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An asymptotic method for constructing the Poincaré mapping in describing the transition of dynamical chaos in Hamiltonian systems. (English)
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6 January 2004
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The Cauchy problem for a system with one degree of freedom is considered. A phase volume conserving mapping is presented by a function of mixed variables (generating function). A parametric method formulates conditions for Hamilton-Jacobi equations. The Hamiltonian is expanded in power series over a small multiplier. Thus an asymptotic Poincaré mapping is found with accuracy up to the third order of magnitude.
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Hamilton-Jacobi equations
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parametric method
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Cauchy problem
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Poincaré mapping
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convergence
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