Approximate solutions of cohomological equations associated with some Anosov flows

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Abstract

The Livshitz theorem reported in 1971 asserts that any C 1 function having zero integrals over all periodic orbits of a topologically transitive Anosov flow is a derivative of another C 1 function in the direction of the flow. Similar results for functions of higher differentiability have also appeared since. In this paper we prove a “finite version“of the Livshitz theorem for a certain class of Anosov flows on 3-dimensional manifolds which include geodesic flows on negatively curved surfaces as a special case.

Original languageEnglish (US)
Pages (from-to)367-379
Number of pages13
JournalErgodic Theory and Dynamical Systems
Volume10
Issue number2
DOIs
StatePublished - Jun 1990

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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