Geometric ergodicity for a class of Markov chains
Geometric Properties of Minimal Surfaces with Free Boundaries.
Geometric realization and coincidence for reducible non-unimodular Pisot tiling spaces with an application to -shifts
This article is devoted to the study of the translation flow on self-similar tilings associated with a substitution of Pisot type. We construct a geometric representation and give necessary and sufficient conditions for the flow to have pure discrete spectrum. As an application we demonstrate that, for certain beta-shifts, the natural extension is naturally isomorphic to a toral automorphism.
Geometric rigidity of invariant measures
Let be a probability measure on which is invariant and ergodic for , and . Let be a local diffeomorphism on some open set. We show that if and , then at -a.e. point . In particular, if is a piecewise-analytic map preserving then there is an open -invariant set containing supp such that is piecewise-linear with slopes which are rational powers of . In a similar vein, for as above, if is another integer and are not powers of a common integer, and if is a -invariant...
Geometry of Markov systems and codimension one foliations
We show that the theory of graph directed Markov systems can be used to study exceptional minimal sets of some foliated manifolds. A C¹ smooth embedding of a contracting or parabolic Markov system into the holonomy pseudogroup of a codimension one foliation allows us to describe in detail the h-dimensional Hausdorff and packing measures of the intersection of a complete transversal with exceptional minimal sets.
Gibbs measures in a markovian context and dimension
The main goal is to use Gibbs measures in a markovian matrices context and in a more general context, to compute the Hausdorff dimension of subsets of [0, 1[ and [0, 1[². We introduce a parameter t which could be interpreted within thermodynamic framework as the variable conjugate to energy. In some particular cases we recover the Shannon-McMillan-Breiman and Eggleston theorems. Our proofs are deeply rooted in the properties of non-negative irreducible matrices and large deviations techniques as...
Gibbs states for non-irreducible countable Markov shifts
We study Markov shifts over countable (finite or countably infinite) alphabets, i.e. shifts generated by incidence matrices. In particular, we derive necessary and sufficient conditions for the existence of a Gibbs state for a certain class of infinite Markov shifts. We further establish a characterization of the existence, uniqueness and ergodicity of invariant Gibbs states for this class of shifts. Our results generalize the well-known results for finitely irreducible Markov shifts.
Gleichmäßige Verteilung von Punkten in gewissen metrischen Räumen, speziell auf der Kugel.
Global-Local subadditive ergodic theorems and application to homogenization in elasticity
Goodwyn's theorem for sequential entropy on pseudocompact spaces
Gradient flows with metric and differentiable structures, and applications to the Wasserstein space
In this paper we summarize some of the main results of a forthcoming book on this topic, where we examine in detail the theory of curves of maximal slope in a general metric setting, following some ideas introduced in [11, 5], and study in detail the case of the Wasserstein space of probability measures. In the first part we derive new general conditions ensuring convergence of the implicit time discretization scheme to a curve of maximal slope, the uniqueness, and the error estimates. In the second...
Gradients of Borel functions
Gradual doubling property of Hutchinson orbits
The classical self-similar fractals can be obtained as fixed points of the iteration technique introduced by Hutchinson. The well known results of Mosco show that typically the limit fractal equipped with the invariant measure is a (normal) space of homogeneous type. But the doubling property along this iteration is generally not preserved even when the starting point, and of course the limit point, both have the doubling property. We prove that the elements of Hutchinson orbits possess the doubling...
Graphen reeller Funktionen.
Group Automorphisms With Finite Entropy.
Group ideals in a semigroup of measures.
Group valued, α-additive set functions
Groupes engendrés par des ensembles compacts Lebesgue-négligeables
Groups Admitting Ergodic Actions with Generalized Discrete Spectrum.
Groups of Measure Preserving Transformations.