Brake orbits for Hamiltonian systems of the classical type via geodesics in singular Finsler metrics
We consider Hamiltonian functions of the classical type, namely, even and convex with respect to the generalized momenta. A brake orbit is a periodic solution of Hamilton’s equations such that the generalized momenta are zero on two different points. Under mild assumptions, this paper reduces the mu...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2022-03-01
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| Series: | Advances in Nonlinear Analysis |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/anona-2022-0222 |
| _version_ | 1817997633057193984 |
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| author | Corona Dario Giannoni Fabio |
| author_facet | Corona Dario Giannoni Fabio |
| author_sort | Corona Dario |
| collection | DOAJ |
| description | We consider Hamiltonian functions of the classical type, namely, even and convex with respect to the generalized momenta. A brake orbit is a periodic solution of Hamilton’s equations such that the generalized momenta are zero on two different points. Under mild assumptions, this paper reduces the multiplicity problem of the brake orbits for a Hamiltonian function of the classical type to the multiplicity problem of orthogonal geodesic chords in a concave Finslerian manifold with boundary. This paper will be used for a generalization of a Seifert’s conjecture about the multiplicity of brake orbits to Hamiltonian functions of the classical type. |
| first_indexed | 2024-04-14T02:39:58Z |
| format | Article |
| id | doaj.art-5962a2a3de134ee280f07551166b8709 |
| institution | Directory Open Access Journal |
| issn | 2191-950X |
| language | English |
| last_indexed | 2024-04-14T02:39:58Z |
| publishDate | 2022-03-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advances in Nonlinear Analysis |
| spelling | doaj.art-5962a2a3de134ee280f07551166b87092022-12-22T02:17:09ZengDe GruyterAdvances in Nonlinear Analysis2191-950X2022-03-011111223124810.1515/anona-2022-0222Brake orbits for Hamiltonian systems of the classical type via geodesics in singular Finsler metricsCorona Dario0Giannoni Fabio1School of Science and Technology, Mathematics Division, University of Camerino, 62032 Camerino, ItalySchool of Science and Technology, Mathematics Division, University of Camerino, 62032 Camerino, ItalyWe consider Hamiltonian functions of the classical type, namely, even and convex with respect to the generalized momenta. A brake orbit is a periodic solution of Hamilton’s equations such that the generalized momenta are zero on two different points. Under mild assumptions, this paper reduces the multiplicity problem of the brake orbits for a Hamiltonian function of the classical type to the multiplicity problem of orthogonal geodesic chords in a concave Finslerian manifold with boundary. This paper will be used for a generalization of a Seifert’s conjecture about the multiplicity of brake orbits to Hamiltonian functions of the classical type.https://doi.org/10.1515/anona-2022-0222hamiltonian systemsbrake orbitsfinsler metricvariational methods70h1270g7570h0558e1053b40 |
| spellingShingle | Corona Dario Giannoni Fabio Brake orbits for Hamiltonian systems of the classical type via geodesics in singular Finsler metrics Advances in Nonlinear Analysis hamiltonian systems brake orbits finsler metric variational methods 70h12 70g75 70h05 58e10 53b40 |
| title | Brake orbits for Hamiltonian systems of the classical type via geodesics in singular Finsler metrics |
| title_full | Brake orbits for Hamiltonian systems of the classical type via geodesics in singular Finsler metrics |
| title_fullStr | Brake orbits for Hamiltonian systems of the classical type via geodesics in singular Finsler metrics |
| title_full_unstemmed | Brake orbits for Hamiltonian systems of the classical type via geodesics in singular Finsler metrics |
| title_short | Brake orbits for Hamiltonian systems of the classical type via geodesics in singular Finsler metrics |
| title_sort | brake orbits for hamiltonian systems of the classical type via geodesics in singular finsler metrics |
| topic | hamiltonian systems brake orbits finsler metric variational methods 70h12 70g75 70h05 58e10 53b40 |
| url | https://doi.org/10.1515/anona-2022-0222 |
| work_keys_str_mv | AT coronadario brakeorbitsforhamiltoniansystemsoftheclassicaltypeviageodesicsinsingularfinslermetrics AT giannonifabio brakeorbitsforhamiltoniansystemsoftheclassicaltypeviageodesicsinsingularfinslermetrics |