Realization of Period Maps of Planar Hamiltonian Systems |
| |
Authors: | Carlos Rocha |
| |
Institution: | (1) Centro de Análise Matemática, Geometria e Sistemas Dinamicos, Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa, Portugal |
| |
Abstract: | We consider the set of 2π-periodic solutions of the ordinary differential equation u′′ + g(u) = 0 for a nonlinearity , satisfying a dissipative condition of the form for , and under the generic assumption that the potential G, given by , is a Morse function. Under these assumptions, we characterize the period maps realizable by planar Hamiltonian systems of
the form . Considering the Morse type of G, the set of periodic orbits in the phase space is decomposed into disks and annular regions. Then, the realizable period maps are described in terms of sets of sequences
of positive integers corresponding to the lap numbers of the 2π-periodic solutions. This leads to a characterization of the
classes of Morse–Smale attractors that are realizable by dissipative semilinear parabolic equations of the form defined on the circle, .
|
| |
Keywords: | Classification of attractors nonlinear boundary value problems Morse– Smale systems |
本文献已被 SpringerLink 等数据库收录! |
|