×

zbMATH — the first resource for mathematics

Entropy and exponential growth of \(\pi _ 1\) in dimension two. (English) Zbl 0644.58016
Summary: The authors show that if \(f: M\to M\) is a \(C^{1+\alpha}\) diffeomorphism of a compact surface and if the topological entropy of f is positive then there is a finite invariant set P such that the map induced by f on \(\pi_ 1(M-P)\) has exponential growth.

MSC:
37D99 Dynamical systems with hyperbolic behavior
37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory, local dynamics
28D20 Entropy and other invariants
PDF BibTeX XML Cite
Full Text: DOI