Related papers: Belinskaya's theorem is optimal
We show that the equations which describe irreversible evolution of a system can be derived from a variational principle. We suggest a Lagrangian, which depends on the properties of the normal and the so-called "mirror-image" system. The…
In the present paper we prove that for any open connected set $\Omega\subset{\mathbb R}^{n+1}$, $n\geq 1$, and any $E\subset \partial\Omega$ with $0<{\mathcal H}^n(E)<\infty$ absolute continuity of the harmonic measure $\omega$ with respect…
We characterize the points that satisfy Birkhoff's ergodic theorem under certain computability conditions in terms of algorithmic randomness. First, we use the method of cutting and stacking to show that if an element x of the Cantor space…
We study nonhyperbolic and transitive partially hyperbolic diffeomorphisms having a one-dimensional center. We prove joint flexibility with respect to entropy and center Lyapunov exponent for a broad class of these systems. Flexibility…
We prove that for semi-invertible and H\"older continuous linear cocycles $A$ acting on an arbitrary Banach space and defined over a base space that satisfies the Anosov Closing Property, all exceptional Lyapunov exponents of $A$ with…
In this paper, we define the so-called square entropy and prove that n-to-1 full zip shift maps are intrinsically ergodic. Furthermore, we show that square entropy characterizes uniform n-to-1 transformations of $(m,l)$-Bernoulli type that…
In this paper we prove the following theorem. Let L/\Q_p be a finite extension with ring of integers O_L and maximal ideal lambda. Theorem 1. Suppose that p >= 5. Suppose also that \rho:G_\Q -> GL_2(O_L) is a continuous representation…
In \cite{Ch91a} it was shown that the billiard ball map for the periodic Lorentz gas has infinite topological entropy. In this article we study the set of points with infinite Lyapunov exponents. Using the cell structure developed in…
A P\'olya-Szeg\"o inequality for the circular rearrangement is proven, under general assumptions. In addition, sufficient conditions are given, under which all the extremals of the inequality are symmetric.
Oseledets' celebrated Multiplicative Ergodic Theorem (MET) is concerned with the exponential growth rates of vectors under the action of a linear cocycle on R^d. When the linear actions are invertible, the MET guarantees an…
A Lagrangian description of a maximally supersymmetric conformal field theory in three dimensions was constructed recently by Bagger and Lambert (BL). The BL theory has SO(4) gauge symmetry and contains scalar and spinor fields that…
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 investigate the Brolin's theorem over $\mathbb{H}$, the skew field of quaternions. Moreover, considering a quaternionic polynomial $p$ with real coefficients, we focus on the properties of its equilibrium measure, among the…
In this paper, we prove an $L^2$ extension theorem with optimal estimate in a precise way, which implies optimal estimate versions of various well-known $L^2$ extension theorems. As applications, we give proofs of a conjecture of Suita on…
We say that two free probability-measure-preserving actions of countable groups are Shannon orbit equivalent if there is an orbit equivalence between them whose associated cocycle partitions have finite Shannon entropy. We show that if the…
We provide a direct proof of Agafonov's theorem which states that finite state selection preserves normality. We also extends this result to the more general setting of shifts of finite type by defining selections which are compatible the…
In this paper we introduce and explore the notion of rigidity group, associated with a collection of finitely many sequences, and show that this concept has many, somewhat surprising characterizations of algebraic, spectral, and unitary…
These notes contain an Ergodic-theoretic account of the Cocycle Superrigidity Theorem recently discovered by Sorin Popa. We state and prove a relative version of the result, discuss some applications to measurable equivalence relations, and…
In this paper, we investigate capacity preserving transformations and their ergodicity. We show that for any measurable transformation $\theta$ there always exists a $\theta$-invariant capacity. We investigate some limit properties under…
We develop a new method, based on pluripotential theory, to study the transfer (Perron-Frobenius) operator induced on $\mathbb P^k = \mathbb P^k (\mathbb C)$ by a holomorphic endomorphism and a suitable continuous weight. This method allows…