Federico Rodriguez Hertz
Rigidity of real-analytic actions of $SL(n,\Z)$ on $\T^n$: A case of realization of Zimmer program.
Втр, 02/16/2010 - 16:01 — SomNambulAuthors: Anatole Katok, Federico Rodriguez Hertz
Subjects: Dynamical Systems
AbstractWe prove that any real-analytic action of $SL(n,\Z), n\ge 3$ with standard
homotopy data that preserves an ergodic measure $\mu$ whose support is not
contained in a ball, is analytically conjugate on an open invariant set to the
standard linear action on the complement to a finite union of periodic orbits.Measure and cocycle rigidity for certain non-uniformly hyperbolic actions of higher rank abelian groups.
Пт, 01/15/2010 - 16:01 — SomNambulAuthors: Anatole Katok, Federico Rodriguez Hertz
Subjects: Dynamical Systems
AbstractWe prove absolute continuity of "high entropy" hyperbolic invariant measures
for smooth actions of higher rank abelian groups assuming that there are no
proportional Lyapunov exponents. For actions on tori and infranilmanifolds
existence of an absolutely continuous invariant measure of this kind is
obtained for actions whose elements are homotopic to those of an action by
hyperbolic automorphisms with no multiple or proportional Lyapunov exponents.
In the latter case a form of rigidity is proved for certain natural classes of
cocycles over the action.
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