NONUNIFORM MEASURE RIGIDITY (2009)
Boris Kalinin, Anatole Katok, Federico Rodriguez Hertz
Abstract. We consider an ergodic invariant measure µ for a smooth action α of Z k, k ≥ 2, on a (k +1)-dimensional manifold or for a locally free smooth action of R k, k ≥ 2 on a (2k +...
Nonuniform measure rigidity (2008)
Kalinin, Boris, Katok, Anatole, Hertz, Federico Rodriguez
We consider an ergodic invariant measure $\mu$ for a smooth action of $Z^k$, $k \ge 2$, on a $(k+1)$-dimensional manifold or for a locally free smooth action of $R^k$, $k \ge 2$ on a...
Global rigidity of certain abelian actions by toral automorphisms (2006)
We prove global rigidity results for some linear abelian actions on tori. The type of actions we deal with includes in particular maximal rank semisimple actions on $\T^N$.
Stable ergodicity of certain linear automorphisms of the torus (2005)
We find a class of ergodic linear automorphisms of $\T^N$ that are stably ergodic. This class includes all non-Anosov ergodic automorphisms when $N=4$. As a corollary, we obtain the fact that all...
Dynamics in the isotopy class of a pseudo-Anosov map (2004)
Hertz, Federico Rodriguez, Hertz, Jana Rodriguez, Ures, Raul
Despite its homotopical stability, new relevant dynamics appear in the isotopy class of a pseudo-Anosov homeomorphism. We study these new dynamics by identifying homotopically equivalent orbits,...
DYNAMICS IN THE ISOTOPY CLASS OF A PSEUDO-ANOSOV MAP (2004)
Federico Rodriguez Hertz, Jana Rodriguez Hertz, Raúl Ures
Abstract. Despite its homotopical stability, new relevant dynamics appear in the isotopy class of a pseudo-Anosov homeomorphism. We study these new dynamics by identifying homotopically equivalent...
On the geodesic flow of surfaces of nonpositive curvature (2003)
Let $S$ be a surface of nonpositive curvature of genus bigger than 1 (i.e. not the torus). We prove that any flat strip in the surface is in fact a flat cylinder. Moreover we prove that the number of...
Stable ergodicity of certain linear automorphisms of the torus (2002)
We prove that some ergodic linear automorphisms of $\T^N$ are stably ergodic, i.e. any small perturbation remains ergodic. The class of linear automorphisms we deal with includes all non-Anosov...