Approximate solutions of cohomological equations associated with some Anosov flows

Research output: Contribution to journalArticle

4 Citations (Scopus)

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 - Jan 1 1990

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Anosov Flow
Approximate Solution
Curved Surface
Geodesic Flow
Differentiability
Theorem
Periodic Orbits
Orbits
Derivatives
Derivative
Zero

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

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Approximate solutions of cohomological equations associated with some Anosov flows. / Katok, Svetlana.

In: Ergodic Theory and Dynamical Systems, Vol. 10, No. 2, 01.01.1990, p. 367-379.

Research output: Contribution to journalArticle

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