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Italo Cipriano

Publications and source records attributed to Italo Cipriano.

8 recordsLinked to original sources
arXiv2021

Time change for flows and thermodynamic formalism

This paper is devoted to study how do thermodynamic formalism quantities varies for time changes of suspension flows defined over countable Markov shifts. We prove that in general no quantity is preserved. We also make a topological description of the space of suspension flows according to certain thermodynamic quantities. For example, we show that the set of suspension flows defined over the full shift on a countable alphabet having finite entropy is open. Of independent interest might be a set of analytic tools we use to construct examples with prescribed thermodynamic behaviour.

math.DS↗
arXiv2019

Approximating integrals with respect to stationary probability measures of iterated function systems

We study fast approximation of integrals with respect to stationary probability measures associated to iterated functions systems on the unit interval. We provide an algorithm for approximating the integrals under certain conditions on the iterated function system and on the function that is being integrated. We apply this technique to estimate Hausdorff moments, Wasserstein distances and Lyapunov exponents of stationary probability measures.

math.DS↗
arXiv2019

$Δ$-transitivity for several transformations and an application to the coboundary problem

Given a compact and complete metric space $X$ with several continuous transformations $T_1, T_2, \ldots T_H: X \to X,$ we find sufficient conditions for the existence of a point $x\in X$ such that $(x,x,\ldots,x)\in X^H$ has dense orbit for the transformation $$\mathcal T:=T_1\times T_2\times\cdots\times T_H.$$ We use these conditions together with Livšic theorem, to obtain that for $α$-Hölder maps $f_1,f_2,\ldots,f_H: X\to \mathbb{R},$ the product $\prod_{i=1}^H f_i(x_i)$ is a smooth coboundary with respect to $\mathcal T$ is equivalent to the existence of a non-empty open subset $U \subset X$ such that $$\sup_{N} \sup_{x\in U}\left| \sum_{j=0}^{N} \prod_{i=1}^H f_i (T_i^{j} x) \right| < \infty.$$

math.DS↗
arXiv2018

The Wasserstein distance between stationary measures associated to iterated function schemes on the unit interval

We provide explicit formulaes for the first Kantorovich-Wasserstein distance between stationary measures for iterated function scheme on the unit interval. In particular, we consider two stationary measures with different configurations of the weights associated to the same iterated function schemes with disjoint images composed of: $k$ positive contractions or $2$ contractions of different sign. We also study the case of two stationary measures associated to different iterated function schemes.

math.DS↗
arXiv2016

The smoothness of the stationary measure

We study the smoothness of the stationary measure with respect to smooth perturbations of the iterated function scheme and the weight functions that define it. Our main theorems relate the smoothness of the perturbation of: the iterated function scheme and the weight functions; to the smoothness of the perturbation of the stationary measure. The results depend on the smoothness of: the iterated function scheme and the weights functions; and the space on which the stationary measure acts as a linear operator. As a consequence we also obtain the smoothness of the Hausdorff dimension of the limit set and of the Hausdorff dimension of the stationary measure.

math.DS↗
arXiv2016

A Large deviation and an escape rate result for special semi-flows

In this paper we consider a smooth flow $(Λ,Φ^t)$ builded from suspending over a (non-invertible topologically mixing) subshift of finite type, and we equip it with an equilibrium measure $ν$ on $Λ.$ The two main theorems are a large deviation and an escape rate result. The first theorem gives an explicit formula for $X>0$ and $Y$ such that $$ν\left\{x\inΛ: \left|\int F\circ Φ^s (x) ds-\int F dμ\right|>ε\right\}\leq \exp(-Xt+\log t+Y)$$ for $t\gg>1\ggε>0,$ where $F:Λ\to\mathbb{R}$ is smooth. The second theorem gives an explicit lower bound for the asymptotic behaviour of the escape rate of $ν$ through a small hole.

math.DS↗
arXiv2016

Entry time statistics to different shrinking sets

We consider $ψ$-mixing dynamical systems $(\mathcal{X},T,B,μ)$ and we find conditions on families of sets $\{\mathcal{U}_n\subset \mathcal{X}:n\in\mathbb{N}\}$ so that $μ(\mathcal{U}_n)τ_n$ tends in law to an exponential random variable, where $τ_n$ is the entry time to $\mathcal{U}_n.$

math.DS↗