Advanced search
Start date
(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Systems of Transversal Sections Near Critical Energy Levels of Hamiltonian Systems in R-4

Full text
de Paulo, Naiara V. [1] ; Salomao, Pedro A. S. [2]
Total Authors: 2
[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
Document type: Journal article
Source: MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY; v. 252, n. 1202, p. 1+, MAR 2018.
Web of Science Citations: 0

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-Doctorate
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