Related papers: Lifting Measures to Inducing Schemes

The main result of this note, Theorem 2, is the following: a Borel measure on the space of infinite Hermitian matrices, that is invariant under the action of the infinite unitary group and that admits well-defined projections onto the…

Bowen showed that a continuous expansive map with specification has a unique measure of maximal entropy. We show that the conclusion remains true under weaker non-uniform versions of these hypotheses. To this end, we introduce the notions…

We study continuity and discontinuity of the upper and lower (modified) box-counting, Hausdorff, packing, (modified) correlation measure-dimension mappings under the weak, setwise and TV topology on the space of Borel measures respectively…

Borel probability measures living on metric spaces are fundamental mathematical objects. There are several meaningful distance functions that make the collection of the probability measures living on a certain space a metric space. We are…

We prove a pointwise ergodic theorem for quasi-probability-measure-preserving (quasi-pmp) locally countable measurable graphs, equivalently, Schreier graphs of quasi-pmp actions of countable groups. For ergodic graphs, the theorem gives an…

Ergodic optimization aims to describe dynamically invariant probability measures that maximize the integral of a given function. For a wide class of intrinsically ergodic subshifts over a finite alphabet, we show that the space of…

We consider classes of dynamical systems admitting Markov induced maps. Under general assumptions, which in particular guarantee the existence of SRB measures, we prove that the entropy of the SRB measure varies continuously with the…

We study distributions of persistent homology barcodes associated to taking subsamples of a fixed size from metric measure spaces. We show that such distributions provide robust invariants of metric measure spaces, and illustrate their use…

We analyze a class of piecewise linear parabolic maps on the torus, namely those obtained by considering a linear map with double eigenvalue one and taking modulo one in each component. We show that within this two parameter family of maps,…

Packing topological entropy is a dynamical analogy of the packing dimension, which can be viewed as a counterpart of Bowen topological entropy. In the present paper, we will give a systematically study to the packing topological entropy for…

We study a measure-theoretic notion of connectedness for sets of finite perimeter in the setting of doubling metric measure spaces supporting a weak $(1,1)$-Poincar\'{e} inequality. The two main results we obtain are a decomposition theorem…

The dynamics of symbolic systems, such as multidimensional subshifts of finite type or cellular automata, are known to be closely related to computability theory. In particular, the appropriate tools to describe and classify topological…

Let $f : X\to X$ be a dominating meromorphic map on a compact K\"ahler manifold $X$ of dimension $k$. We extend the notion of topological entropy $h^l_{\mathrm{top}}(f)$ for the action of $f$ on (local) analytic sets of dimension $0\leq l…

This paper provides rates of convergence for empirical (generalised) barycenters on compact geodesic metric spaces under general conditions using empirical processes techniques. Our main assumption is termed a variance inequality and…

Let $f$ be an holomorphic endomorphism of $\mathbb{C}\mathbb{P}^k$. We construct by using coding techniques a class of ergodic measures as limits of non-uniform probability measures on preimages of points. We show that they have large…

We consider the action of $SL(2,\mathbb{R})$ on a vector bundle $\mathbf{H}$ preserving an ergodic probability measure $\nu$ on the base $X$. Under an irreducibility assumption on this action, we prove that if $\hat\nu$ is any lift of $\nu$…

We introduce two parametrized families of piecewise affine maps on $[0,1]^2$ and $[0,1]^3$, as generalizations of the heterochaos baker maps which were introduced and investigated in [Y. Saiki, H. Takahasi, J. A. Yorke, Nonlinearity, 34…

On a one-sided shift of finite type we prove that for a generic Holder continuous function there is a unique maximizing measure. We show that b-Holder continuous functions can be approximated in the a-Holder topology, a<b, by a function…

Hierarchy of one-parameter families of chaotic maps with an invariant measure have been introduced, where their appropriate coupling has lead to the generation of some coupled chaotic maps with an invariant measure. It is shown that these…

Let $k \ge 1$ be an integer and $f$ a holomorphic endomorphism of $\mathbb P^k (\mathbb C)$ of algebraic degree $d\geq 2$. We introduce a volume dimension for ergodic $f$-invariant probability measures with strictly positive Lyapunov…