相关论文: Ergodic Deviations of Degenerate Multidimensional …

We show the existence of a limiting distribution $\cD_\cC$ of the adequately normalized discrepancy function of a random translation on a torus relative to a strictly convex set $\cC$. Using a correspondence between the small divisors in…

Based on T.Tao's result of norm convergence of multiple ergodic averages for commut-ing transformation, we obtain there is a subsequence which converges almost everywhere. Meanwhile, the ergodic behaviour, which the time average is equal to…

The main result of this paper is a decomposition theorem for a measure on the one-dimensional torus. Given a sufficiently large subset $S$ of the positive integers, an arbitrary measure on the torus is decomposed as the sum of two measures.…

We show how to construct certain homogeneous deformations for rational normal varieties with codimension one torus action. This can then be used to construct homogeneous deformations of any toric variety in arbitrary degree. For locally…

We provide a construction of examples of semistable degeneration via toric geometry. The applications include a higher dimensional generalization of classical degeneration of K3 surface into 4 rational components, an algebraic geometric…

We describe the deformation space of a solid torus with boundary modelled on convex ideal hyperbolic polyhedra. This deformation space is given by natural Gauss--Bonnet type inequalities on the dihedral angles. The result extends to solid…

The stochastic 2D Navier-Stokes equations on the torus driven by degenerate noise are studied. We characterize the smallest closed invariant subspace for this model and show that the dynamics restricted to that subspace is ergodic. In…

We study two sorts of actions on the space of conjugacy classes of irreducible $SU_2$-representations of a knot group. One of them is an involution which comes from the algebraic structure of $SU_2$ and the other is the action by the outer…

We study ergodic averages for a class of pseudodifferential operators on the flat N-dimensional torus with respect to the Schr\"odinger evolution. The later can be consider a quantization of the geodesic flow on $\bT^N$. We prove that, up…

We consider isometric actions of lattices in semisimple algebraic groups on (possibly non-compact) homogeneous spaces with (possibly infinite) invariant Radon measure. We assume that the action has a dense orbit, and demonstrate two novel…

Let $X$ be a 3-dimensional affine variety with a faithful action of a 2-dimensional torus $T$. Then the space of first order infinitesimal deformations $T^1(X)$ is graded by the characters of $T$, and the zeroth graded component $T^1(X)_0$…

We prove that all ergodic automorphisms of the $N$-dimensional torus with two dimensional center are stably ergodic. This includes all ergodic automorphisms in dimension $N\leq 5$ or $N=7$. This generalizes a previous result of…

We study double ergodic averages with respect to two general commuting transformations and establish a sharp quantitative result on their convergence in the norm. We approach the problem via real harmonic analysis, using recently developed…

I formulate a deformation of the dimensional-regularization technique that is useful for theories where the common dimensional regularization does not apply. The Dirac algebra is not dimensionally continued, to avoid inconsistencies with…

We investigate U(1)-equivariant deformations of C. LeBrun's self-dual metric with torus action. We explicitly determine all U(1)-subgroups of the torus for which one can obtain U(1)-equivariant deformation that do not preserve semi-free…

Deviation of ergodic sums is studied for substitution dynamical systems with a matrix that admits eigenvalues of modulus 1. We consider the corresponding eigenfunctions, and in Theorem 1.1 we prove that the limit inferior of the ergodic…

We prove a general result about the decomposition on ergodic components of group actions on boundaries of spherically homogeneous rooted trees. Namely, we identify the space of ergodic components with the boundary of the orbit tree…

In this paper, for a discontinuous skew-product transformation with the integrable observation function, we obtain uniform ergodic theorem and semi-uniform ergodic theorem. The main assumptions are that discontinuity sets of transformation…

Given a polyhedral cone sigma with smooth two-dimensional faces and, moreover, a lattice point R in the dual cone of sigma, we describe the part of the versal deformation of the associated toric variety TV(sigma) that is built from the…

Periods of parallel exterior forms define natural coordinates on the deformation space of complete affine structures on the two-torus. These coordinates define a differentiable structure on this deformation space, under which it is…