Report
Integrable Hamiltonian systems with a periodic orbit or invariant torus unique in the whole phase space
| العنوان: | Integrable Hamiltonian systems with a periodic orbit or invariant torus unique in the whole phase space |
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| المؤلفون: | Sevryuk, Mikhail B. |
| المصدر: | Arnold Mathematical Journal, 2018, Vol. 4, No. 3-4, pp. 415-422 |
| سنة النشر: | 2018 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Dynamical Systems, 37J45 70H12 70K42 70K43 70H33 |
| الوصف: | 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 |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1007/s40598-018-0093-2 |
| URL الوصول: | http://arxiv.org/abs/1808.03596 |
| رقم الانضمام: | edsarx.1808.03596 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1007/s40598-018-0093-2 |
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