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Expanding repellers in limit sets for iterations of holomorphic functions

Feliks Przytycki (2005)

Fundamenta Mathematicae

We prove that for Ω being an immediate basin of attraction to an attracting fixed point for a rational mapping of the Riemann sphere, and for an ergodic invariant measure μ on the boundary FrΩ, with positive Lyapunov exponent, there is an invariant subset of FrΩ which is an expanding repeller of Hausdorff dimension arbitrarily close to the Hausdorff dimension of μ. We also prove generalizations and a geometric coding tree abstract version. The paper is a continuation of a paper in Fund. Math. 145...

Explicit computations of all finite index bimodules for a family of II 1 factors

Stefaan Vaes (2008)

Annales scientifiques de l'École Normale Supérieure

We study II 1 factors M and N associated with good generalized Bernoulli actions of groups having an infinite almost normal subgroup with the relative property (T). We prove the following rigidity result : every finite index M - N -bimodule (in particular, every isomorphism between M and N ) is described by a commensurability of the groups involved and a commensurability of their actions. The fusion algebra of finite index M - M -bimodules is identified with an extended Hecke fusion algebra, providing the...

Explicit Teichmüller curves with complementary series

Carlos Matheus, Gabriela Weitze-Schmithüsen (2013)

Bulletin de la Société Mathématique de France

We construct an explicit family of arithmetic Teichmüller curves 𝒞 2 k , k ∈ ℕ , supporting SL ( 2 , ℝ ) -invariant probabilities μ 2 k such that the associated SL ( 2 , ℝ ) -representation on  L 2 ( 𝒞 2 k , μ 2 k ) has complementary series for every k ≥ 3 . Actually, the size of the spectral gap along this family goes to zero. In particular, the Teichmüller geodesic flow restricted to these explicit arithmetic Teichmüller curves 𝒞 2 k has arbitrarily slow rate of exponential mixing.

Exponential convergence to the stationary measure and hyperbolicity of the minimisers for random Lagrangian Systems

Boritchev, Alexandre (2017)

Proceedings of Equadiff 14

We consider a class of 1d Lagrangian systems with random forcing in the spaceperiodic setting: φ t + φ x 2 / 2 = F ω , x ∈ S 1 = ℝ / ℤ . These systems have been studied since the 1990s by Khanin, Sinai and their collaborators [7, 9, 11, 12, 15]. Here we give an overview of their results and then we expose our recent proof of the exponential convergence to the stationary measure [6]. This is the first such result in a classical setting, i.e. in the dual-Lipschitz metric with respect to the Lebesgue space L p for finite p , partially answering...

Exponential decay to partially thermoelastic materials

Jaime E. Muñoz Rivera, Vanilde Bisognin, Eleni Bisognin (2002)

Bollettino dell'Unione Matematica Italiana

We study the thermoelastic system for material which are partially thermoelastic. That is, a material divided into two parts, one of them a good conductor of heat, so there exists a thermoelastic phenomenon. The other is a bad conductor of heat so there is not heat flux. We prove for such models that the solution decays exponentially as time goes to infinity. We also consider a nonlinear case.

Exponential functionals of brownian motion and class-one Whittaker functions

Fabrice Baudoin, Neil O’Connell (2011)

Annales de l'I.H.P. Probabilités et statistiques

We consider exponential functionals of a brownian motion with drift in ℝn, defined via a collection of linear functionals. We give a characterisation of the Laplace transform of their joint law as the unique bounded solution, up to a constant factor, to a Schrödinger-type partial differential equation. We derive a similar equation for the probability density. We then characterise all diffusions which can be interpreted as having the law of the brownian motion with drift conditioned on the law of...

Exponential inequalities and functional central limit theorems for random fields

Jérôme Dedecker (2001)

ESAIM: Probability and Statistics

We establish new exponential inequalities for partial sums of random fields. Next, using classical chaining arguments, we give sufficient conditions for partial sum processes indexed by large classes of sets to converge to a set-indexed brownian motion. For stationary fields of bounded random variables, the condition is expressed in terms of a series of conditional expectations. For non-uniform φ -mixing random fields, we require both finite fourth moments and an algebraic decay of the mixing coefficients....

Exponential inequalities and functional central limit theorems for random fields

Jérôme Dedecker (2010)

ESAIM: Probability and Statistics

We establish new exponential inequalities for partial sums of random fields. Next, using classical chaining arguments, we give sufficient conditions for partial sum processes indexed by large classes of sets to converge to a set-indexed Brownian motion. For stationary fields of bounded random variables, the condition is expressed in terms of a series of conditional expectations. For non-uniform ϕ-mixing random fields, we require both finite fourth moments and an algebraic decay of the mixing coefficients. ...

Exponential limit shadowing

S. A. Ahmadi, M. R. Molaei (2013)

Annales Polonici Mathematici

We introduce the notion of exponential limit shadowing and show that it is a persistent property near a hyperbolic set of a dynamical system. We show that Ω-stability implies the exponential limit shadowing property.

Exponential mixing for the Teichmüller flow

Artur Avila, Sébastien Gouëzel, Jean-Christophe Yoccoz (2006)

Publications Mathématiques de l'IHÉS

We study the dynamics of the Teichmüller flow in the moduli space of abelian differentials (and more generally, its restriction to any connected component of a stratum). We show that the (Masur-Veech) absolutely continuous invariant probability measure is exponentially mixing for the class of Hölder observables. A geometric consequence is that the S L ( 2 , ℝ ) action in the moduli space has a spectral gap.

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