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.


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.
Full Text: DOI Euclid