6533b862fe1ef96bd12c6916

RESEARCH PRODUCT

Minimal number of periodic orbits for nonsingular Morse-Smale flows in odd dimension

M. A. BertolimC. BonattiM. P. MelloG. M. Vago

subject

[MATH] Mathematics [math][MATH]Mathematics [math]Mathematics::Algebraic TopologyMathematics::Symplectic GeometryMathematics::Geometric Topology

description

We compute the minimal number p_min of closed orbits of any Morse-Smale flow on any compact odd-dimensional manifold with boundary in terms of some given homological information. The underlying algorithm is based on optimization theory in network flows and transport systems. Such a number p_min is a lower bound in the general case but we provide, for any initial homological data, a Morse-Smale model for which p_min is attained. We also apply our techniques to the problem of the continuation of Lyapnov graphs to Lyapnov graphs of Smale type.

yearjournalcountryeditionlanguage
2020-09-23
https://hal.science/hal-02946281