Propriedades de dinâmica hamiltoniana em níveis de energia convexos de R4 / Properties of the hamiltonian dynamics in convex energy levels of R4
AUTOR(ES)
Marcelo Ribeiro de Resende Alves
DATA DE PUBLICAÇÃO
2011
RESUMO
The existence of global surfaces of section to ows is of central importance in the theory of dynamical systems, as a global surface of section simplies the study of the dynamics of a ow reducing it to the study of the dynamics of a dieomorphism. We present in detail the construction due to Hofer, Wysocki and Zehnder (in The dynamics on a strictly convex energy surface in R4) of a global surface of section for the Hamiltonian ow restricted to a convex energy level in R4 . An important consequence of the existence of the global surface of section is that the Hamiltonian ow restricted to a convex energy level in R4 has either 2 or innitely many periodic orbits. This construction makes use of the theory of pseudo-holomorphic curves in symplectizations of contact manifolds developed by the same authors. The arguments also give a new proof of Weinstein conjecture for tight contact forms in S3 .
ASSUNTO(S)
convex energy levels curvas pseudo-holomorfas. global surfaces of section níveis de energia convexos pseudo-holomorphic curves. seções globais
