On the classification of Cartan actions (2009)
Abstract. We study higher rank Cartan actions on compact manifolds preserving an ergodic measure with full support. In particular, we classify actions by R k with k ≥ 3 whose one-parameter groups...
Totally non-symplectic Anosov actions on tori and nilmanifolds (2009)
Fisher, David, Kalinin, Boris, Spatzier, Ralf
We show that sufficiently irreducible totally non-symplectic Anosov actions of higher rank abelian groups on tori and nilmanifolds are $\ci$-conjugate to affine actions.
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 +...
Abstract. The first part of the paper begins with an introduction into Anosov actions of Z k and R k and an overview of the method of studying invariant measures for such actions based on...
Livsic theorem for matrix cocycles (2008)
We prove the Liv\v{s}ic Theorem for arbitrary $GL(m,\mathbb R)$ cocycles. We consider a hyperbolic dynamical system $f : X \to X$ and a H\"older continuous function $A: X \to GL(m,\mathbb R)$. We...
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...
On Anosov diffeomorphisms with asymptotically conformal periodic data (2007)
Kalinin, Boris, Sadovskaya, Victoria
We consider transitive Anosov diffeomorphisms for which every periodic orbit has only one positive and one negative Lyapunov exponent. We establish various properties of such systems including strong...
Boris Kalinin, Anatole Katok, Communicated Ralf Spatzier
ABSTRACT. We prove that every smooth action α of Z k, k ≥ 2, on the (k+ 1)dimensional torus whose elements are homotopic to corresponding elements of an action α0 by hyperbolic linear maps...
On classification of resonance-free Anosov Z^k actions (2006)
Kalinin, Boris, Sadovskaya, Victoria
We consider actions of Z^k, k \ge 2, by Anosov diffeomorphisms which are uniformly quasiconformal on each coarse Lyapunov distribution. These actions generalize Cartan actions for which coarse...
Global rigidity for totally nonsymplectic Anosov Z^k actions (2006)
Kalinin, Boris, Sadovskaya, Victoria
We consider a totally nonsymplectic Anosov action of Z^k which is either uniformly quasiconformal or pinched on each coarse Lyapunov distribution. We show that such an action on a torus is...
Measure rigidity beyond uniform hyperbolicity: Invariant Measures for Cartan actions on Tori (2006)
Kalinin, Boris, Katok, Anatole
We prove that every smooth action of Z^k, k>1, on the (k+1)-dimensional torus homotopic to an action by hyperbolic linear maps preserves an absolutely continuous measure. This is a first known result...
Abstract. We investigate rigidity of measurable structure for higher rank abelian algebraic actions. In particular, we show that ergodic measures for these actions fiber over a 0 entropy measure with...
On the Classification of Cartan Actions (2004)
Kalinin, Boris, Spatzier, Ralf
We study higher rank Cartan actions on compact manifolds preserving an ergodic measure with full support. In particular, we classify actions by $\R ^k$ with $k \geq 3$ whose one-parameter groups act...
Rigidity of the measurable structure for algebraic actions of higher rank abelian groups (2002)
Kalinin, Boris, Spatzier, Ralf
We investigate rigidity of measurable structure for higher rank abelian algebraic actions. In particular, we show that ergodic measures for these actions fiber over a 0 entropy measure with Haar...
Abstract. We investigate joinings of strongly irreducible totally non-symplectic Anosov Z k, k ≥ 2 actions by toral automorphisms. We show that the existence of a non-trivial joining has strong...