Related papers: Monochromatic nonuniform hyperbolicity

Let G be a group, H a hyperbolically embedded subgroup of G, V a normed G-module, U an H-invariant submodule of V. We propose a general construction which allows to extend 1-quasi-cocycles on H with values in U to 1-quasi-cocycles on G with…

We show the existence of large $\mathcal C^1$ open sets of area preserving endomorphisms of the two-torus which have no dominated splitting and are non-uniformly hyperbolic, meaning that Lebesgue almost every point has a positive and a…

We present an example of a discontinuity point for the Lyapunov exponents when viewed as a function of the cocycle in a topology finer than the $C^0$-topology. The linear cocycle taking values in SL(2,R) is locally constant, defined over a…

In this paper, we prove an inequality, which we call "Devroye inequality", for a large class of non-uniformly hyperbolic dynamical systems (M,f). This class, introduced by L.-S. Young, includes families of piece-wise hyperbolic maps…

We prove a geometric criterion on a $\SL$-invariant ergodic probability measure on the moduli space of holomorphic abelian differentials on Riemann surfaces for the non-uniform hyperbolicity of the Kontsevich--Zorich cocycle on the real…

We construct countable Markov partitions for non-uniformly hyperbolic diffeomorphisms on compact manifolds of any dimension, extending earlier work of O. Sarig for surfaces. These partitions allow us to obtain symbolic coding on invariant…

For a large class of transitive non-hyperbolic systems, we construct nonhyperbolic ergodic measures with entropy arbitrarily close to its maximal possible value. The systems we consider are partially hyperbolic with one-dimension central…

In this paper, we pay attention to a weaker version of Walters's question on the existence of non-uniform cocycles for uniquely ergodic minimal dynamical systems on non-degenerate connected spaces. We will classify such dynamical systems…

We prove a rigidity theorem for dominated H\"{o}lder cocycles with values on diffeomorphism groups of a compact manifold over hyperbolic homeomorphisms. More precisely, we show that if two such cocycles have equal periodic data, then they…

Finding a non-sofic hyperbolic group will resolve two major problems in geometric group theory: Are there non sofic groups? Are there non residually finite hyperbolic groups? In this paper, we propose a new probabilistic approach to this…

A theorem of Viana says that almost all cocycles over any hyperbolic system have nonvanishing Lyapunov exponents. In this note we extend this result to cocycles on any noncompact classical semisimple Lie group.

We consider the linear cocycle $(T,A)$ induced by a measure preserving dynamical system $T:X \to X$ and a map $A:X \to \mathit{SL}(2,\mathbb{R})$. We address the dependence of the upper Lyapunov exponent of $(T,A)$ on the dynamics $T$ when…

Making use of the recent theory of noncommutative motives, we prove that every additive invariant satisfies Galois descent. Examples include mixed complexes, Hochschild homology, cyclic homology, periodic cyclic homology, negative cyclic…

We study cohomology of Holder continuous linear cocycles over a hyperbolic dynamical system and regularity of conjugacy between Anosov systems. For cocycles $A$ and $B$ with conjugate periodic data, we establish Holder cohomology under…

In 1970, Hirsch asked what kind of compact invariant sets could be part of a hyperbolic set. Here we obtain that, in case such an invariant set is a 3D manifold, it is a connected sum of tori with handles quotiented by involutions.…

A theorem of Guglielmi and Zennaro implies that if the uniform norm growth of a locally constant GL(2,R)-cocycle on the full shift is not exponential then it must be either bounded or linear, with no other possibilities occurring. We give…

We prove that any k-uniform hypergraph on n vertices with minimum degree at least n/(2(k-1))+o(n) contains a loose Hamilton cycle. The proof strategy is similar to that used by K\"uhn and Osthus for the 3-uniform case. Though some…

We consider Holder continuous fiber bunched GL(d,R)-valued cocycles over an Anosov diffeomorphism. We show that two such cocycles are Holder continuously cohomologous if they have equal periodic data, and prove a result for cocycles with…

Building upon previous works by Young, Chernov-Zhang and Bruin-Melbourne-Terhesiu, we present a general scheme to improve bounds on the statistical properties (in particular, decay of correlations, and rates in the almost sure invariant…

We prove measurable Livsic theorems for dynamical systems modelled by Markov Towers. Our regularity results apply to solutions of cohomological equations posed on Henon-like mappings and a wide variety of nonuniformly hyperbolic systems. We…