Commentarii Mathematici Helvetici

, Volume 57, Issue 1, pp 237–259

Flow equivalence, hyperbolic systems and a new zeta function for flows


  • David Fried
    • University of California

DOI: 10.1007/BF02565860

Cite this article as:
Fried, D. Commentarii Mathematici Helvetici (1982) 57: 237. doi:10.1007/BF02565860


We analyze the dynamics of diffeomorphisms in terms of their suspension flows. For many Axion A diffeomorphisms we find simplest representatives in their flow equivalence class and so reduce flow equivalence to conjugacy. The zeta functions of maps in a flow equivalence class are correlated with a zeta function ζ H for their suspended flow. This zeta function is defined for any flow with only finitely many closed orbits in each homology class, and is proven rational for Axiom A flows. The flow equivalence of Anosov diffeomorphisms is used to relate the spectrum of the induced map on first homology to the existence of fixed points. For Morse-Smale maps, we extend a result of Asimov on the geometric index.

Copyright information

© Birkhäuser Verlag 1982