A report on an ergodic dichotomy
Resumen:
We establish (some directions of) a Ledrappier correspondence between Hölder cocycles, Patterson–Sullivan measures, etc for word-hyperbolic groups with metric-Anosov Mineyev flow. We then study Patterson–Sullivan measures for ϑ-Anosov representations over a local field and show that these are parameterized by the ϑ-critical hypersurface of the representation. We use these Patterson–Sullivan measures to establish a dichotomy concerning directions in the interior of the ϑ-limit cone of the representation in question: if u is such a half-line, then the subset of u-conical limit points has either total mass if |ϑ| ≤ 2 or zero mass if |ϑ| ≥ 4. The case |ϑ| = 3 remains unsettled.
| 2024 | |
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ANOSOV REPRESENTATIONS PATTERSON–SULLIVAN MEASURES SKEW-PRODUCTS OVER SUBSHIFTS |
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| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/44989 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución (CC - By 4.0) |
