Approximate solutions of cohomological equations associated with some Anosov flows

Svetlana Katok

doi:10.1017/S0143385700005605

Approximate solutions of cohomological equations associated with some Anosov flows

Svetlana Katok

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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 language	English (US)
Pages (from-to)	367-379
Number of pages	13
Journal	Ergodic Theory and Dynamical Systems
Volume	10
Issue number	2
DOIs	https://doi.org/10.1017/S0143385700005605
State	Published - Jun 1990

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

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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.",

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