Elliptic bindings for dynamically convex Reeb flows on the real projective three-space

Autor(es)

Hryniewicz, Umberto L. ^[1] ; Salomao, Pedro A. S. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Fed Rio de Janeiro, Dept Matemat Aplicada, Av Athos da Silveira Ramos 149, BR-21941909 Rio De Janeiro, RJ - Brazil

^[2] Univ Sao Paulo, Dept Matemat, Inst Matemat & Estat, Rua Matao, 1010 Cidade Univ, BR-05508090 Sao Paulo, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS; v. 55, n. 2 APR 2016.
• Citações Web of Science: 1

Resumo

The first result of this paper is that every contact form on RP3 sufficiently C-infinity-close to a dynamically convex contact form admits an elliptic-parabolic closed Reeb orbit which is 2-unknotted, has self-linking number -1/2 and transverse rotation number in (1/2, 1]. Our second result implies that any p-unknotted periodic orbit with self-linking number -1/p of a dynamically convex Reeb flow on a lens space of order p is the binding of a rational open book decomposition, whose pages are global surfaces of section. As an application we show that in the planar circular restricted three-body problem for energies below the first Lagrange value and large mass ratio, there is a special link consisting of two periodic trajectories for the massless satellite near the smaller primary-lunar problem-with the same contact-topological and dynamical properties of the orbits found by Conley (Commun Pure Appl Math 16: 449-467, 1963) for large negative energies. Both periodic trajectories bind rational open book decompositions with disk-like pages which are global surfaces of section. In particular, one of the components is an elliptic-parabolic periodic orbit. (AU)

• Processo FAPESP: 13/20065-0 - Dinâmica simplética em dimensão 3
• Beneficiário: Pedro Antonio Santoro Salomão
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 11/16265-8 - Dinâmica em baixas dimensões
• Beneficiário: Edson Vargas
• Modalidade de apoio: Auxílio à Pesquisa - Temático