An obstruction to the existence of certain dynamics in surface diffeomorphisms

Paul Blanchard, John M Franks

Research output: Contribution to journalArticle

5 Scopus citations

Abstract

Let M be a two-dimensional, compact manifold and g:Μ→ΜM be a diffeomorphism with a hyperbolic chain recurrent set. We find restrictions on the reduced zeta function p(t) of anyzero-dimensional basic set of g. If deg (p(t)) is odd, then p(1) = 0 (in Z/2Z). Since there are infinitely many subshifts of finite type whose reduced zeta functions do not satisfy these restrictions, there are infinitely many subshifts which cannot be basic sets for any diffeomorphism of any surface.

Original languageEnglish (US)
Pages (from-to)255-260
Number of pages6
JournalErgodic Theory and Dynamical Systems
Volume1
Issue number3
DOIs
StatePublished - Jan 1 1981

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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