Dynamical Systems with Cross-sections
نویسندگان
چکیده
The problem of classifying dynamical systems (flows) with global cross-sections in terms of the associated diffeomorphisms of the crosssections is considered. Suppose that, for i = 1,2, ty is a C flow (r > 0) on the Cr manifold M¡ that admits a global cross-section 5, Q M¡ with associated diffeomorphism ('first return map') d¡. If rank (HX(MX ;Z)) = 1, then (Mx,2) if and only if dx is Cs conjugate to d2. If rank (//, (A/, ;Z)) ¥= 1 and x has a periodic orbit, then there are infinitely many global cross-sections T¡ Q Mx of $x, such that the associated diffeomorphisms are pairwise nonconjugate.
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