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arXiv · 2012.01808

Counting periodic orbits of vector fields over smooth closed manifolds

Eaman Eftekhary
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Abstract

We address the problem of counting periodic orbits of vector fields on smooth closed manifolds. The space of non-constant periodic orbits is enlarged to a complete space by adding the ghost orbits, which are decorations of the zeros of vector fields. Associated with any compact and open subset $\Gamma$ of the moduli space of periodic and ghost orbits, we define an integer weight. When the vector field moves along a path, and $\Gamma$ deforms in a compact and open family, we show that the weight function stays constant. We also give a number of examples and computations, which illustrate the applications of our main theorem.

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Eaman Eftekhary. 2020-12-03. Counting periodic orbits of vector fields over smooth closed manifolds. https://arxiv.org/abs/2012.01808

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