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 | |
| State | Published - Jan 1 1990 |
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All Science Journal Classification (ASJC) codes
- Mathematics(all)
- Applied Mathematics
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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 journal › Article
TY - JOUR
T1 - Approximate solutions of cohomological equations associated with some Anosov flows
AU - Katok, Svetlana
PY - 1990/1/1
Y1 - 1990/1/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84972003864&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84972003864&partnerID=8YFLogxK
U2 - 10.1017/S0143385700005605
DO - 10.1017/S0143385700005605
M3 - Article
AN - SCOPUS:84972003864
VL - 10
SP - 367
EP - 379
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
SN - 0143-3857
IS - 2
ER -