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Periods of continuous maps on closed surfaces. (English) Zbl 1379.37085

Summary: The objective of the present work is to present information on the set of periodic points of a continuous self-map on a closed surface which can be obtained using the action of this map on homological groups of the closed surface.

MSC:

37E30 Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces
37C05 Dynamical systems involving smooth mappings and diffeomorphisms
37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics
37C30 Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc.
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