Annales Academić Scientiarum Fennicć
Mathematica
Volumen 35, 2010, 503-513

TOPOLOGICAL ENTROPY AND DIFFEOMORPHISMS OF SURFACES WITH WANDERING DOMAINS

Ferry Kwakkel and Vladimir Markovic

University of Warwick, Mathematics Institute
Zeeman Building, Coventry CV4 7AL, United Kingdom; F.H.Kwakkel 'at' warwick.ac.uk

University of Warwick, Mathematics Institute
Zeeman Building, Coventry CV4 7AL, United Kingdom; V.Markovic 'at' warwick.ac.uk

Abstract. Let M be a closed surface and f a diffeomorphism of M. A diffeomorphism is said to permute a dense collection of domains, if the union of the domains are dense and the iterates of any one domain are mutually disjoint. In this note, we show that if f \in Diff^1+\alpha(M), with \alpha > 0, and permutes a dense collection of domains with bounded geometry, then f has zero topological entropy.

2000 Mathematics Subject Classification: Primary 30C62; Secondary 28D20.

Key words: Quasiconformal mappings, entropy, wandering domains.

Reference to this article: F. Kwakkel and V. Markovic: Topological entropy and diffeomorphisms of surfaces with wandering domains. Ann. Acad. Sci. Fenn. Math. 35 (2010), 503-513.

Full document as PDF file

doi:10.5186/aasfm.2010.3531