Seminário de Sistemas Dinâmicos 2023/2

Seminário 4: 31/10/2023

Título do seminário: On the minimal number of periodic orbits for nonsingular Morse-Smale flows
Ministrante: Profa. Dra. Gioia Vago - Université de Bourgogne
Data: 31/10/2023
Horário: 11h
Local: Auditório do IME

Resumo: We consider the couples $(M, \Phi)$ where $M$ is an odd-dimensional compact manifolds with boundary, endowed with a non-singular Morse-Smale flow~$\Phi$, satisfying some \emph{given} homological boundary information. We compute, in terms of such given homological information, a number $p_{min}$ such that \emph{any} non-singular Morse-Smale flow~$\Phi$ on any manifold~$M$ satisfying the given abstract homological data must have \emph{at least} $p_{min}$ closed periodic orbits. Moreover, we can provide, for any initial homological data, a Morse Smale model $(M_0, \Phi_0)$ for which $p_{min}$ is attained. Note that in the general case of a couple $(M, \Phi)$ satisfying the given homological information, such a number $p_{min}$ is a lower bound.

Ref.: M.A. BERTOLIM, C. BONATTI, M. MELLO, G.M. VAGO, Minimal number of periodic orbits for nonsingular Morse-Smale flows in odd dimension.