The Multiplicity Problem for Periodic Orbits of Magnetic Flows on the 2-Sphere Full article
| Journal |
Advanced Nonlinear Studies
ISSN: 1536-1365 , E-ISSN: 2169-0375 |
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| Output data | Year: 2017, Volume: 17, Pages: 17-30 Pages count : 14 DOI: 10.1515/ANS-2016-6003 | ||||||||||
| Tags | Hamiltonian Systems; Magnetic Flows; Mañé Critical Values; Periodic Orbits; Tonelli Lagrangians | ||||||||||
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Abstract:
We consider magnetic Tonelli Hamiltonian systems on the cotangent bundle of the 2-sphere, where the magnetic form is not necessarily exact. It is known that, on very low and on high energy levels, these systems may have only finitely many periodic orbits. Our main result asserts that almost all energy levels in a precisely characterized intermediate range (e_0,e_1) possess infinitely many periodic orbits. Such a range of energies is non-empty, for instance, in the physically relevant case where the Tonelli Lagrangian is a kinetic energy and the magnetic form is oscillating (in which case, e_0=0 is the minimal energy of the system).
Cite:
Abbondandolo A.
, Asselle L.
, Benedetti G.
, Mazzucchelli M.
, Taimanov I.A.
The Multiplicity Problem for Periodic Orbits of Magnetic Flows on the 2-Sphere
Advanced Nonlinear Studies. 2017. V.17. P.17-30. DOI: 10.1515/ANS-2016-6003 WOS Scopus OpenAlex
The Multiplicity Problem for Periodic Orbits of Magnetic Flows on the 2-Sphere
Advanced Nonlinear Studies. 2017. V.17. P.17-30. DOI: 10.1515/ANS-2016-6003 WOS Scopus OpenAlex
Dates:
| Submitted: | Aug 12, 2016 |
| Accepted: | Nov 4, 2016 |
| Published print: | Dec 1, 2016 |
| Published online: | Feb 1, 2017 |
Identifiers:
| Web of science: | WOS:000398552700003 |
| Scopus: | 2-s2.0-85011634303 |
| OpenAlex: | W2526672374 |