| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Univ Fed Santa Catalina, Dept Matemat, Rua Joao Pessoa 2750, BR-\~{} AO Bairro Velha Blumenau, SC - Brazil
[2] Univ Sao Paulo, Inst Matemat & Estat, Dept Matemat, Rua Matao 1010, Sao Paulo, SP - Brazil
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY; v. 252, n. 1202, p. 1+, MAR 2018. |
| Web of Science Citations: | 0 |
| Abstract | |
In this article we study Hamiltonian flows associated to smooth functions H : R-4 -> R restricted to energy levels close to critical levels. We assume the existence of a saddle-center equilibrium point p(c) in the zero energy level H-1( 0). The Hamiltonian function near p(c) is assumed to satisfy Moser's normal form and pc is assumed to lie in a strictly convex singular subset S-0 of H-1(0). Then for all E > 0 small, the energy level H-1(E) contains a subset S-E near S-0, diffeomorphic to the closed 3-ball, which admits a system of transversal sections F-E, called a 2 - 3 foliation. F-E is a singular foliation of SE and contains two periodic orbits P-2,P-E subset of partial derivative S-E and P-3,P-E subset of S-E \textbackslash{} partial derivative S-E as binding orbits. P-2,P-E is the Lyapunoff orbit lying in the center manifold of p(c), has Conley-Zehnder index 2 and spans two rigid planes in partial derivative S-E. P-3,P-E has Conley-Zehnder index 3 and spans a one parameter family of planes in S-E \textbackslash{} partial derivative S-E. A rigid cylinder connecting P-3,P-E to P-2,P-E completes F-E. All regular leaves are transverse to the Hamiltonian vector field. The existence of a homoclinic orbit to P-2,P-E in S-E \textbackslash{} partial derivative S-E follows from this foliation. (AU) | |
| FAPESP's process: | 09/18586-6 - Hamiltonian dynamics near critical energy levels and homoclinic orbits to the central manifold of a saddle-center |
| Grantee: | Naiara Vergian de Paulo |
| Support Opportunities: | Scholarships in Brazil - Doctorate |
| FAPESP's process: | 14/08113-1 - Systems of transverse sections in classical mechanics |
| Grantee: | Naiara Vergian de Paulo |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 11/16265-8 - Low dimensional dynamics |
| Grantee: | Edson Vargas |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 13/20065-0 - Symplectic dynamics in dimension 3 |
| Grantee: | Pedro Antonio Santoro Salomão |
| Support Opportunities: | Regular Research Grants |