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) |
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Pages (from-to) | 367-379 |
Number of pages | 13 |
Journal | Ergodic Theory and Dynamical Systems |
Volume | 10 |
Issue number | 2 |
DOIs | |
State | Published - Jun 1990 |
All Science Journal Classification (ASJC) codes
- Mathematics(all)
- Applied Mathematics