Related papers: Remarks on step cocycles over rotations, centraliz…

We define a cocycle on the group of symplectic diffeomorphisms of a symplectic manifold and investigate its properties. The main applications are concerned with symplectic actions of discrete groups. For example, we give an alternative…

We prove the so called Liv\v{s}ic theorem for cocycles taking values in the group of $C^{1+\beta}-diffeomorphisms of any closed manifold of arbitrary dimension. Since no localization hypothesis is assumed, this result is completely global…

A convergence theorem is obtained for quantum random walks with particles in an arbitrary normal state. This result unifies and extends previous work on repeated-interactions models, including that of the author (2010, J. London Math. Soc.…

We let $\varphi$ be an ageometric fully irreducible outer automorphism so that its Handel-Mosher axis bundle consists of a single unique axis. We show that the centralizer $Cen(\langle\varphi\rangle)$ of the cyclic subgroup generated by…

Given two relatively prime positive integers $\alpha$ and $\beta$, we consider simple lattice paths (with unit East and unit North steps) from $(0,0)$ to $(\alpha k,\beta k)$, and enumerate them by their left and right bounces with respect…

We prove some properties of analytic multiplicative and sub-multiplicative cocycles. The results allow to construct natural invariant analytic sets associated to complex dynamical systems.

Using a complex parameterizing rational spherical chains, we construct explicit cocycles for $\mathrm{GL}_n(\Q)$ valued in the motivic cohomology of (open subsets of) the algebraic $n$-torus $\mathbb{G}_m^n$. The resulting cocycles directly…

We study the problem of lifting various mixing properties from a base automorphism $T\in {\rm Aut}\xbm$ to skew products of the form $\tfs$, where $\va:X\to G$ is a cocycle with values in a locally compact Abelian group $G$,…

The Diophantine sums $\sum_{n=1}^N \| n \alpha \|^{-1}$ and $\sum_{n=1}^N n^{-1} \| n \alpha \|^{-1}$ appear in many different areas including the ergodic theory of circle rotations, lattice point counting and random walks, often in…

We consider a piecewise analytic real expanding map $f: [0,1]\to [0,1]$ of degree $d$ which preserves orientation, and a real analytic positive potential $g: [0,1] \to \mathbb{R}$. We assume the map and the potential have a complex analytic…

Let $\Gamma^+$ be the positive cone in a totally ordered abelian group $\Gamma$, and let $\alpha$ be an action of $\Gamma^+$ by endomorphisms of a $C^*$-algebra $A$. We consider a new kind of crossed-product $C^*$-algebra…

It is known that the generating function associated with the enumeration of non-backtracking walks on finite graphs is a rational matrix-valued function of the parameter; such function is also closely related to graph-theoretical results…

For every $3/4\le \delta, \beta< 1$ satisfying $\delta\leq \beta < \frac{1+\delta}{2}$ we construct a finitely generated group $\Gamma$ and a (symmetric, finitely supported) random walk $X_n$ on $\Gamma$ so that its expected distance from…

This is the first paper in a series where we study arithmetic applications of the multiple elliptic Gamma functions originated from mathematical physics. The main purpose of this paper is the introduction of a framework for applications of…

We prove a multiplicative ergodic theorem for bistochastic completely positive (bcp) linear cocycles acting on finite-dimensional matrix algebras, giving an invariant splitting described explicitly in terms of the multiplicative domains of…

We compute the group cohomology of $32\Gamma_3f$, a certain group of order 32. For this we construct explicit cocycle representatives of the cohomology generators. We thus lay to rest a discrepancy between several published computations of…

We propose a generalization of the classical theta function to higher cohomology of the polarization line bundle on a family of complex tori with positive index. The constructed cocycles vary horizontally with respect to the (projective)…

A result for subadditive ergodic cocycles is proved that provides more delicate information than Kingman's subadditive ergodic theorem. As an application we deduce a multiplicative ergodic theorem generalizing an earlier result of…

In this paper we present a geometric way to extend the Shintani lift from even weight cusp forms for congruence subgroups to arbitrary modular forms, in particular Eisenstein series. This is part of our efforts to extend in the noncompact…

In this paper, we construct higher Chow cycles of type $(2, 1)$ on a family of surfaces related to a product of curves, which are certain degree $N$ abelian covers of $\mathbb{P}^1$ branched over $n+2$ points. We prove that for a very…