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Markov families for Anosov flows with an involutive action

Published online by Cambridge University Press:  22 January 2016

Toshiaki Adachi
Toshiaki Adachi*
Affiliation:
Depertment of Mathematics, Nagoya University, Chikusa-ku, Nagoya 464, Japan
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The aim of this note is to construct “involutive” Markov families for geodesic flows of negative curvature. Roughly speaking, a Markov family for a flow is a finite family of local cross-sections to the flow with fine boundary conditions. They are basic tools in the study of dynamical systems. In 1973, R. Bowen [5] constructed Markov families for Axiom A flows. Using these families, he reduced the problem of counting periodic orbits of an Axiom A flow to the case of hyperbolic symbolic flows.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 104 , December 1986 , pp. 55 - 62
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1986

References

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