Integrable Hamiltonian systems with a periodic orbit or invariant torus unique in the whole phase space
| Autor: | Sevryuk, Mikhail B. |
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| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Arnold Mathematical Journal, 2018, Vol. 4, No. 3-4, pp. 415-422 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s40598-018-0093-2 |
| Popis: | It is very well known that periodic orbits of autonomous Hamiltonian systems are generically organized into smooth one-parameter families (the parameter being just the energy value). We present a simple example of an integrable Hamiltonian system (with an arbitrary number of degrees of freedom greater than one) with a unique periodic orbit in the phase space (which is not compact). Similar examples are given for Hamiltonian systems with a unique invariant torus (of any prescribed dimension) carrying conditionally periodic motions. Parallel examples for Hamiltonian systems with a compact phase space and with uniqueness replaced by isolatedness are also constructed. Finally, reversible analogues of all the examples are described. Comment: 8 pages, submitted to the Arnold Mathematical Journal |
| Databáze: | arXiv |
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