Related papers: Invariant measure for double base expansions

We prove that for any given modulus of continuity {\omega} there exist (uncountably many) C1 uniformly expanding maps of the circle whose derivatives have $C^1$ as an optimal modulus of continuity and which preserve an invariant probability…

In this paper we study systems of $N$ uniformly expanding coupled maps when $N$ is finite but large. We introduce self-consistent transfer operators that approximate the evolution of measures under the dynamics, and quantify this…

This paper generalizes the results of [13] and then provides an interesting example. We construct a family of $W$-like maps $\{W_a\}$ with a turning fixed point having slope $s_1$ on one side and $-s_2$ on the other. Each $W_a$ has an…

In this paper we consider continued fraction (CF) expansions on intervals different from $[0,1]$. For every $x$ in such interval we find a CF expansion with a finite number of possible digits. Using the natural extension, the density of the…

We obtain large deviation results for non-uniformly expanding maps with non-flat singularities or criticalities and for partially hyperbolic non-uniformly expanding attracting sets. That is, given a continuous function we consider its space…

We analyze invariant measures of two coupled piecewise linear and everywhere expanding maps on the synchronization manifold. We observe that though the individual maps have simple and smooth functions as their stationary densities, they…

We analyze certain parametrized families of one-dimensional maps with infinitely many critical points from the measure-theoretical point of view. We prove that such families have absolutely continuous invariant probability measures for a…

We consider random perturbations of non-uniformly expanding maps, possibly having a non-degenerate critical set. We prove that, if the Lebesgue measure of the set of points failing the non-uniform expansion or the slow recurrence to the…

We utilize Gaussian measure preserving systems to prove the existence and genericity of Lebesgue measure preserving transformations $T:[0,1]\rightarrow [0,1]$ which exhibit both mixing and rigidity behavior along families of asymptotically…

We consider some classes of piecewise expanding maps in finite dimensional spaces having invariant probability measures which are absolutely continuous with respect to Lebesgue measure. We derive an entropy formula for such measures and,…

In this paper, building on previous work, we extend the thermodynamic formalism for random open dynamical systems generated by piecewise monotone interval maps with countably many branches. Under summable and contracting assumptions on the…

We express continuous $\times p,\times q$-invariant measures on the unit circle via some simple forms. On one hand, a continuous $\times p,\times q$-invariant measure is the weak-$*$ limit of average of Dirac measures along an irrational…

We derive new variants of the quantitative Borel--Cantelli lemma and apply them to analysis of statistical properties for some dynamical systems. We consider intermittent maps of $(0,1]$ which have absolutely continuous invariant…

The paper analyzes a specific class of random walks on quotients of $X:=\text{SL}(k,{\Bbb R})/ \Gamma$ for a lattice $\Gamma$. Consider a one parameter diagonal subgroup, $\{g_t\}$, with an associated abelian expanding horosphere, $U\cong…

For random piecewise linear systems T of the interval that are expanding on average we construct explicitly the density functions of absolutely continuous T-invariant measures. In case the random system uses only expanding maps our…

We prove stochastic stability of absolutely continuous invariant measures (ACIMs) for piecewise expanding $C^{1+\varepsilon}$ maps of the interval. For maps $\tau$ in the class $\mathcal{T}([0,1]; s, \varepsilon)$, we consider perturbed…

We construct an invariant measure for a piecewise analytic interval map whose Lyapunov exponent is not defined. Moreover, for a set of full measure, the pointwise Lyapunov exponent is not defined. This map has a Lorenz-like singularity and…

Let $I\subset (0,\infty )$ be an interval that is closed with respect to the multiplication. The operations $C_{f,g}\colon I^{2}\rightarrow I$ of the form \begin{equation*} C_{f,g}\left( x,y\right) =\left( f\circ g\right) ^{-1}\left(…

For piecewise $C^1$ interval maps possibly containing critical points and discontinuities with negative Schwarzian derivative, under two summability conditions on the growth of the derivative and recurrence along critical orbits, we prove…

The standard map, paradigmatic conservative system in the $(x,p)$ phase space, has been recently shown to exhibit interesting statistical behaviors directly related to the value of the standard map parameter $K$. A detailed numerical…