On the use of the topological degree theory in broken orbits analysis

Pokrovskii, A.; Rasskazov, O.

doi:10.1090/S0002-9939-03-07036-9

On the use of the topological degree theory in broken orbits analysis
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by A. V. Pokrovskii and O. A. Rasskazov PDF

Proc. Amer. Math. Soc. 132 (2004), 567-577 Request permission

Abstract:

Dynamical systems $f$ in ${\mathbb R}^{d}$ are studied. Let $\mathbf {\Omega } \subset \mathbb {R}^{d}$ be a bounded open set. We will be interested in those periodic orbits such that at least one of its points lies inside $\mathbf {\Omega }$ and at least one of its points lies outside $\mathbf {\overline {\Omega }}$; the orbits with this property are called $\mathbf {\Omega }$-broken. Information about the structure of the set of $\mathbf {\Omega }$-broken orbits is suggested; results are formulated in terms of topological degree theory.

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