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Periods, Lefschetz numbers and entropy for a class of maps on a bouquet of circles. (English) Zbl 1162.37303
Summary: We consider some smooth maps on a bouquet of circles. For these maps we can compute the number of fixed points, the existence of periodic points and an exact formula for topological entropy. We use Lefschetz fixed point theory and actions of our maps on both the fundamental group and the first homology group.

MSC:
37B40 Topological entropy
37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics
37C35 Orbit growth in dynamical systems
37E25 Dynamical systems involving maps of trees and graphs
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