Related papers: On lifting invariant probability measures

We study some special classes of piecewise continuous maps on a finite smooth partition of a compact manifold and look for invariant measures for such maps. We show that in the simplest one-dimensional case (so-called interval translation…

In this paper we study the liftability property for piecewise continuous maps of compact metric spaces, which admit inducing schemes in the sense of Pesin and Senti [PS05, PS06]. We show that under some natural assumptions on the inducing…

We show that recurrence conditions do not yield invariant Borel probability measures in the descriptive set-theoretic milieu, in the strong sense that if a Borel action of a locally compact Polish group on a standard Borel space satisfies…

Given a closed orientable surface (\Sigma) of genus at least two, we establish an affine isomorphism between the convex compact set of isotopy-invariant topological measures on (\Sigma) and the convex compact set of additive functions on…

A Borel probability measure $\mu$ on a locally compact group is called a spectral measure if there exists a subset of continuous group characters which forms an orthogonal basis of the Hilbert space $L^2(\mu)$. In this paper, we…

Sets of invariant measures are considered for continuous maps of a metric compact set. We take Kantorovich metric to calculate distance between measures and Hausdorff metrics to calculate distance between compact sets. Consider the function…

We study the problem of lifting a measure to an induced map $F(x)=f^{R(x)}(x)$. In particular, we give a necessary and sufficient condition for an ergodic $f$ invariant probability $\mu$ to be $F$-liftable as well as a condition for the…

For polynomials $f$ on the complex plane with a dendrite Julia set we study invariant probability measures, obtained from a reference measure. To do this we follow Keller in constructing canonical Markov extensions. We discuss…

For a homeomorphism $T$ on a compact metric space $X$, a $T$-invariant Borel probability measure $\mu$ on $X$ and a measure-theoretic quasifactor $\widetilde{\mu}$ of $\mu$, we study the relationship between the local entropy of the system…

Here we shall consider the topology and dynamics associated to a wide class of matchbox manifolds, including a large selection of tiling spaces and all minimal matchbox manifolds of dimension one. For such spaces we introduce topological…

Building on recent results regarding symmetric probabilistic constructions of countable structures, we provide a method for constructing probability measures, concentrated on certain classes of countably infinite structures, that are…

For a compact metric space $X$ with a group $G$ acting on it continuously, an invariant random compact is a Borel probability measure on the space of nonempty compact subsets of $X$ that is invariant under the action of $G$. The action is…

Let $X$ be a zero-dimensional compact metrizable space endowed with a strictly positive continuous Borel $\sigma$-additive measure $\mu$ which is good in the sense that for any clopen subsets $U,V\subset X$ with $\mu(U)<\mu(V)$ there is a…

It is well known that the space of invariant probability measures for transitive sub-shifts of finite type is a Poulsen simplex. In this article we prove that in the non-compact setting, for a large family of transitive countable Markov…

We say that $f:[0,1]\to [0,1]$ is a {\it piecewise continuous interval map} if there exists a partition $0=x_0<x_1<\cdots<x_{d}<x_{d+1}=1$ of $[0,1]$ such that $f\vert_{(x_{i-1},x_i)}$ is continuous and the lateral limits $w_0^+=\lim_{x\to…

Standard results in descriptive set theory provide sufficient conditions for a Borel set $P \subseteq \mathbb{N}^\mathbb{N} \times \mathbb{N}^\mathbb{N}$ to admit a Borel uniformization, namely, when $P$ has "small" sections or "large"…

We prove that a homeomorphism of a compact metric space has an expansive measure \cite{ms} if and only if it has many ones with invariant support. We also study homeomorphisms for which the expansive measures are dense in the space of Borel…

Motivated by recent investigations of Sophie Grivaux and \'Etienne Matheron on the existence of invariant measures in Linear Dynamics, we introduce the concept of locally bounded orbit for a continuous linear operator $T:X\longrightarrow X$…

We are interested in Filippov systems which preserve a probability measure on a compact manifold. We define a measure to be invariant for a Filippov system as the natural analogous definition of invariant measure for flows. Our main result…

We consider dynamical systems $T: X \to X$ that are extensions of a factor $S: Y \to Y$ through a projection $\pi: X \to Y$ with shrinking fibers, i.e. such that $T$ is uniformly continuous along fibers $\pi^{-1}(y)$ and the diameter of…