Related papers: Non-ergodicity for C^1 Expanding Maps

We develop non-invertible Pesin theory for a new class of maps called cusp maps. These maps may have unbounded derivative, but nevertheless verify a property analogous to $C^{1+\epsilon}$. We do not require the critical points to verify a…

We construct ergodic probability measures with infinite metric entropy for typical continuous maps and homeomorphisms on compact manifolds. We also construct sequences of such measures that converge to a zero-entropy measure.

In this article we intend to contribute in the understanding of the ergodic properties of the set RT of robustly transitive local diffeomorphisms on a compact manifold M without boundary. We prove that there exists a C^1 residual subset R_0…

We consider random iteration of exponential entire functions, i.e. of the form ${\mathbb C}\ni z\mapsto f_\lambda(z):=\lambda e^z\in\mathbb C$, $\lambda\in{\mathbb C}\setminus \{0\}$. Assuming that $\lambda$ is in a bounded closed interval…

Any ergodic measure of a smooth map on a compact manifold has a multifractal spectrum with one point - the dimension of the measure itself - at the diagonal. We will construct examples where this fails in the most drastic way for invariant…

In this paper, we establish a coupling lemma for standard families in the setting of piecewise expanding interval maps with countably many branches. Our method merely requires that the expanding map satisfies Chernov's one-step expansion at…

We consider partially hyperbolic diffeomorphisms $f$ with a one-dimensional central direction such that the unstable entropy exceeds the stable entropy. Our main result proves that such maps have a finite number of ergodic measures of…

For random compositions of independent and identically distributed measurable maps on a Polish space, we study the existence and finitude of absolutely continuous ergodic stationary probability measures (which are, in particular, physical…

We construct SRB measures for endomorphisms satisfying conditions far weaker than the non-uniformly expansion. As a consequence, the definition of non-uniformly expanding map can be weakened. We also prove the existence of an absolutely…

We describe a construction process of a relevant measure in any non-empty compact metric space. This probability measure has invariance properties with respect to isometric maps defined on open sets. These properties imply that this measure…

We consider a piecewise smooth expanding map of the interval possessing two invariant subsets of positive Lebesgue measure and exactly two ergodic absolutely continuous invariant probability measures (ACIMs). When this system is perturbed…

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…

Given a pair $Q=(q_0,q_1)\in(1,\infty)^2$ with $q_0+q_1\ge q_0q_1$, a sequence $(c_i)\in\set{0,1}^\infty$ is called a $Q$-expansion of $x$ if<br/>\begin{equation*}<br/>x=\sum_{i=1}^{\infty}\frac{c_i}{q_{c_1}\cdots…

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…

We study ergodic properties of a family of traffic maps acting in the space of bi-infinite sequences of real numbers. The corresponding dynamics mimics the motion of vehicles in a simple traffic flow, which explains the name. Using…

We study invariant measures of a piecewise expanding map in $\mathbb{R}^m$ defined by an expanding similitude modulo lattice. Using the result of Bang on a problem of Tarski, we show that when the similarity ratio is not less than $m+1$, it…

We show that a strengthened version of the Collet-Eckmann condition for multimodal maps is topologically invariant. In particular, if f is non-uniformly expanding and the critical points are generic with respect to the absolutely continuous…

There is only one fully supported ergodic invariant probability measure for the adic transformation on the space of infinite paths in the graph that underlies the Eulerian numbers. This result may partially justify a frequent assumption…

A unified view is given to recent developments about a systematic method of constructing rational mappings as ergodic transformations with non-uniform invariant measures on the unit interval I=[0,1]. All of the rational ergodic mappings of…

In this paper we study the relationship between Lyapunov exponents and the induced map on cohomology for $C^{1}-$diffeomorphisms on compact manifolds. We show that if the induced map on cohomology has spectral radius strictly larger than 1,…