Ergodic properties and flexibility of Lyapunov exponents for partially hyperbolic ...
Decay of correlations and statistical properties for geodesic flows in nonpositive...
| Full text | |
| Author(s): |
Agafonov, Sergey I.
;
Alves, Thais G. P.
Total Authors: 2
|
| Document type: | Journal article |
| Source: | ADVANCES IN GEOMETRY; v. 24, n. 2, p. 11-pg., 2024-04-25. |
| Abstract | |
We prove that if the geodesic flow on a surface has an integral which is fractional-linear in momenta, then the dimension of the space of such integrals is either 3 or 5, the latter case corresponding to constant gaussian curvature. We give also a geometric criterion for the existence of fractional-linear integrals: such an integral exists if and only if the surface carries a geodesic 4-web with constant cross-ratio of the four directions tangent to the web leaves. (AU) | |
| FAPESP's process: | 22/12813-5 - Webs of positive rank with prescribed geometry |
| Grantee: | Serguei Agafonov |
| Support Opportunities: | Regular Research Grants |