Generation of one-sided random dynamical systems by stochastic differential equations.
Generators for Amenable Group Actions.
Generators of an Abelian Group of Invertible Measure-Preserving Transformations.
Generators of perfect σ-algebras of -actions
Generic points in the cartesian powers of the Morse dynamical system
The symbolic dynamical system associated with the Morse sequence is strictly ergodic. We describe some topological and metrical properties of the Cartesian powers of this system, and some of its other self-joinings. Among other things, we show that non generic points appear in the fourth power of the system, but not in lower powers. We exhibit various examples and counterexamples related to the property of weak disjointness of measure preserving dynamical systems.
Generic Properties of Continuous Iterated Function Systems with Place Dependent Probabilities
It is shown that for a typical continuous learning system defined on a compact convex subset of ℝⁿ the Hausdorff dimension of its invariant measure is equal to zero.
Generic Properties of Invariant Measures for Continous Piecewise Monotonic Transformations.
Generic smooth cocycles of degree zero over irrational rotations
If a rotation α of has unbounded partial quotients then “most” of its skew-product diffeomorphic extensions to the 2-torus × defined by cocycles of topological degree zero enjoy nontrivial ergodic properties. In fact they admit a cyclic approximation with speed o(1/n) and have nondiscrete (simple) spectrum. Similar results are obtained for cocycles if α admits a sufficiently good approximation by rationals. For a.e. α and generic cocycles the speed can be improved to o(1/(nlogn)). For generic...
Genericity of nonsingular transformations with infinite ergodic index
It is shown that in the group of invertible measurable nonsingular transformations on a Lebesgue probability space, endowed with the coarse topology, the transformations with infinite ergodic index are generic; they actually form a dense set. (A transformation has infinite ergodic index if all its finite Cartesian powers are ergodic.) This answers a question asked by C. Silva. A similar result was proved by U. Sachdeva in 1971, for the group of transformations preserving an infinite measure. Exploring...
Geometric ergodicity for a class of Markov chains
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.
Global-Local subadditive ergodic theorems and application to homogenization in elasticity
Goodwyn's theorem for sequential entropy on pseudocompact spaces
Group Automorphisms With Finite Entropy.
Groups Admitting Ergodic Actions with Generalized Discrete Spectrum.
Groups of Measure Preserving Transformations.
Groups of Measure Preserving Transformations. II.
Gyration numbers for involutions of subshifts of finite type II.
Gyration numbers for involutions of subshifts of finite type I.
Half-delocalization of eigenfunctions for the Laplacian on an Anosov manifold
We study the high-energy eigenfunctions of the Laplacian on a compact Riemannian manifold with Anosov geodesic flow. The localization of a semiclassical measure associated with a sequence of eigenfunctions is characterized by the Kolmogorov-Sinai entropy of this measure. We show that this entropy is necessarily bounded from below by a constant which, in the case of constant negative curvature, equals half the maximal entropy. In this sense, high-energy eigenfunctions are at least half-delocalized....