GSD Seminar 2023/2

Seminar 4

October 31, 2023

Speaker: Profa. Dra. Gioia Vago - Université de Bourgogne

Title: On the minimal number of periodic orbits for nonsingular Morse-Smale flows

Abstract: 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.

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