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

Autor(es)

de Paulo, Naiara V. ^[1] ; Salomao, Pedro A. S. ^[2]

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY; v. 252, n. 1202, p. 1+, MAR 2018.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 09/18586-6 - Dinâmica Hamiltoniana próxima a níveis críticos e órbitas homoclínicas à variedade central de um sela-centro
• Beneficiário: Naiara Vergian de Paulo
• Modalidade de apoio: Bolsas no Brasil - Doutorado
• Processo FAPESP: 14/08113-1 - Sistemas de seções transversais na mecânica clássica
• Beneficiário: Naiara Vergian de Paulo
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 11/16265-8 - Dinâmica em baixas dimensões
• Beneficiário: Edson Vargas
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 13/20065-0 - Dinâmica simplética em dimensão 3
• Beneficiário: Pedro Antonio Santoro Salomão
• Modalidade de apoio: Auxílio à Pesquisa - Regular