Minimal number of periodic orbits for non-singular Morse–Smale flows in odd dimension
Résumé
We consider the couples (M, 0) where M is an odd-dimensional compact manifold with boundary, endowed with a non-singular Morse-Smale flow 0, satisfying some given homological boundary information. We compute, in terms of that information, a number pmin such that any non-singular Morse-Smale flow 0 on any manifold M satisfying the given abstract homological data must have at least pmin closed periodic orbits. Moreover, we provide, for any initial homological data, a non-singular Morse-Smale model (M0, 00) for which pmin is attained. In the general case of a couple (M, 0) satisfying the given homological information, such a number pmin is a lower bound. The algorithm underlying this computation is based on optimization theory in network flows and transport systems.
Domaines
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Est une version de hal-02946281v2 Preprint M. A. Bertolim, C. Bonatti, M. P. Mello, G. M. Vago. Minimal number of periodic orbits for nonsingular Morse-Smale flows in odd dimension. 2023. ⟨hal-02946281v2⟩