Related papers: Oseledec multiplicative ergodic theorem for lamina…

We give a new proof of the uniformization theorem of the leaves of a lamination by surfaces of hyperbolic conformal type. We use a laminated version of the Ricci flow to prove the existence of a laminated Riemannian metric (smooth on the…

Let~$E$ be a Hilbertian field of characteristic~$0$. R.W.K. Odoni conjectured that for every positive integer~$n$ there exists a polynomial~$f\in E[X]$ of degree~$n$ such that each iterate~$f^{\circ{k}}$ of~$f$ is irreducible and the Galois…

Let (G,+) be a compact, abelian, and metrizable topological group. In this group we take $g\in G$ such that the corresponding automorphism t_g is ergodic. The main result of this paper is a new ergodic theorem for functions in L^1(G,M),…

We show that linearly repetitive weighted Delone sets in groups of polynomial growth have a uniquely ergodic hull. This result applies in particular to the linearly repetitive weighted Delone sets in homogeneous Lie groups constructed in…

We introduce horizontal holonomy groups, which are groups defined using parallel transport only along curves tangent to a given subbundle $D$ of the tangent bundle. We provide explicit means of computing these holonomy groups by deriving…

We show that for a large class of potential functions and big coupling constant $\lambda$ the Schr\"odinger cocycle over the expanding map $x\mapsto bx ~( \text{mod} 1)$ on $\mathbb{T}$ has a Lyapunov exponent $>(\log\lambda)/4$ for all…

For a Riemannian submersion from a simple compact Lie group with a bi-invariant metric, we prove the action of its holonomy group on the fibers is transitive. As a step towards classifying Riemannian submersions with totally geodesic…

We prove a substantial part of a conjecture of Kontsevich and Zorich on the Lyapunov exponents of the Teichmuller geodesic flow on the deviation of ergodic averages for generic conservative flows on higher genus surfaces. The result on the…

This paper is concerned with the study of linear cocycles over uniformly ergodic Markov shifts on a compact space of symbols. We establish the joint H\"older continuity of the maximal Lyapunov exponent as a function of the cocycle and the…

We study the distribution of the angles between Oseledets subspaces and their log-integrability, focusing on dimension $2$. For random i.i.d. products of matrices, we construct examples of probability measures on $\mathrm{GL}_2(\mathbb{R})$…

Given a harmonic measure of a hyperbolic lamination on a compact metric space, a positive harmonic function is defined on the universal cover of a typical leaves. We discuss some properties of this function. Especially if all the leaves are…

The paper is devoted to the properties of a complex matrix ``twisted,'' otherwise called ``spectral,'' cocycle, associated with substitution dynamical systems. Following a recent finding of Rajabzadeh and Safaee [arXiv:2501.16824] of an…

We show how the small perturbations of a linear cocycle have a relative rotation number associated with an invariant measure of the base dynamics an with a $2$-dimensional bundle of the finest dominated splitting (provided that some…

We prove that any smooth foliation that admits a Riemannian foliation structure has a well-defined basic signature, and this geometrically defined invariant is actually a foliated homotopy invariant. We also show that foliated homotopic…

In this paper we study the ergodic theory of a robust non-uniformly expanding maps where no Markov assumption is required. We prove that the topological pressure is differentiable as a function of the dynamics and analytic with respect to…

We survey recent results regarding the study of dynamical properties of the space of positive definite functions and characters of higher rank lattices. These results have several applications to ergodic theory, topological dynamics,…

We revisit certain path-lifting and path-continuation properties of abstract maps as described in the work of F. Browder and R. Rheindboldt in 1950-1960s, and apply their elegant theory to exponential maps. We obtain thereby a number of…

We study the linear cohomological equation in the smooth category over quasi-periodic cocycles in $\mathbb{T} ^{d} \times SU(2)$. We prove that, under a full measure condition on the rotation in $\mathbb{T} ^{d}$, for a generic cocycle in…

Contents 1. Algebraicity criterion: statement 2. Proof of the algebraicity criterion. 3. Pseudoeffectivity and movable classes. 4. Harder-Narasimhan filtrations and pseudo-effectivity. 5. Pseudo-effectivity of relative canonical bundles. 6.…

We scrutinize the geometrical properties of light propagation inside a nonlinear medium modeled by a fully covariant electromagnetic theory in $2+1$-dimensions. After setting the nonlinear constitutive relations, the phase velocity and the…