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A categorical view of Poincaré maps and suspension flows. (English) Zbl 1503.37037

The author discusses Poincaré maps and suspension flows in terms of adjoint pair of functors if categories of dynamical systems are suitably provided. It turns out that the concepts of topological equivalence or topological conjugacy are not sufficient to describe the correspondence. Therefore another category of flows with global Poincaré sections is defined and it is shown that the suspension functor and the Poincaré map functor form an adjoint equivalence in the case of this category.

MSC:

37C10 Dynamics induced by flows and semiflows
37C15 Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems
18F60 Categories of topological spaces and continuous mappings
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References:

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