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Dalia Terhesiu

Publications and source records attributed to Dalia Terhesiu.

At least 37 records · Page 2Linked to original sources
arXiv2020

Limit theorems for wobbly interval intermittent maps

We consider perturbations of interval maps with indifferent fixed points, which we refer to as wobbly interval intermittent maps, for which stable laws for general Hölder observables fail. We obtain limit laws for such maps and Hölder observables. These limit laws are similar to the classical semistable laws previously established for random processes, but certain limitations imposed by the current dynamical set up are reflected in the main result. One of the considered examples is an interval map with a countable number of discontinuities, and to analyse it we need to construct a Markov/Young tower.

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arXiv2020

Local limit theorems for suspended semiflows

We prove local limit theorems for a cocycle over a semiflow by establishing topological, mixing properties of the associated skew product semiflow. We also establish conditional rational weak mixing of certain skew product semiflows and various mixing properties including order 2 rational weak mixing of hyperbolic geodesic flows of cyclic covers.

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arXiv2020

Pressure function and limit theorems for almost Anosov flows

We obtain limit theorems (Stable Laws and Central Limit Theorems, both Gaussian and non-Gaussian) and thermodynamic properties for a class of non-uniformly hyperbolic flows: almost Anosov flows, constructed here. The proofs of the limit theorems for these flows are applications of corresponding theorems in an abstract functional analytic framework, which may be applicable to other classes of non-uniformly hyperbolic flows.

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arXiv2019

Renewal theorems and mixing for non Markov flows with infinite measure

We obtain results on mixing for a large class of (not necessarily Markov) infinite measure semiflows and flows. Erickson proved, amongst other things, a strong renewal theorem in the corresponding i.i.d. setting. Using operator renewal theory, we extend Erickson's methods to the deterministic (i.e. non-i.i.d.) continuous time setting and obtain results on mixing as a consequence. Our results apply to intermittent semiflows and flows of Pomeau-Manneville type (both Markov and nonMarkov), and to semiflows and flows over Collet-Eckmann maps with nonintegrable roof function.

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arXiv2018

Rates of mixing for nonMarkov infinite measure semiflows

We develop an abstract framework for obtaining optimal rates of mixing and higher order asymptotics for infinite measure semiflows. Previously, such results were restricted to the situation where there is a first return Poincaré map that is uniformly expanding and Markov. As illustrations of the method, we consider semiflows over nonMarkov Pomeau-Manneville intermittent maps with infinite measure, and we also obtain mixing rates for semiflows over Collet-Eckmann maps with nonintegrable roof function.

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arXiv2018

Mixing properties for toral extensions of slowly mixing dynamical systems with finite and infinite measure

We prove results on mixing and mixing rates for toral extensions of nonuniformly expanding maps with subexponential decay of correlations. Both the finite and infinite measure settings are considered. Under a Dolgopyat-type condition on nonexistence of approximate eigenfunctions, we prove that existing results for (possibly nonMarkovian) nonuniformly expanding maps hold also for their toral extensions.

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arXiv2018

The pressure function for infinite equilibrium measures

Assume that $(X,f)$ is a dynamical system and $ϕ:X \to [-\infty, \infty)$ is a potential such that the $f$-invariant measure $μ_ϕ$ equivalent to $ϕ$-conformal measure is infinite, but that there is an inducing scheme $F = f^τ$ with a finite measure $μ_{\barϕ}$ and polynomial tails $μ_{\barϕ}(τ\geq n) = O(n^{-β})$, $β\in (0,1)$. We give conditions under which the pressure of $f$ for a perturbed potential $ϕ+sψ$ relates to the pressure of the induced system as $P(ϕ+sψ) = (C P(\overline{ϕ+sψ}))^{1/β} (1+o(1))$, together with estimates for the $o(1)$-error term. This extends results from Sarig to the setting of infinite equilibrium states. We give several examples of such systems, thus improving on the results of Lopes for the Pomeau-Manneville map with potential $ϕ_t = - t\log f'$, as well as on the results by Bruin & Todd on countably piecewise linear unimodal Fibonacci maps. In addition, limit properties of the family of measures $μ_{ϕ+sψ}$ as $s\to 0$ are studied and statistical properties (correlation coefficients and arcsine laws) under the limit measure are derived.

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arXiv2018

Darling-Kac theorem for renewal shifts in the absence of regular variation

We study null recurrent renewal Markov chains with renewal distribution in the domain of geometric partial attraction of a semistable law. Using the classical procedure of inversion, we derive a limit theorem similar to the Darling-Kac law along subsequences and obtain some interesting properties of the limit distribution. Also in this context, we obtain a Karamata type theorem along subsequences for positive operators. In both results, we identify the allowed class of subsequences. We provide several examples of nontrivial infinite measure preserving systems to which these results apply.

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arXiv2017

The Dolgopyat inequality in \BV\ for non-Markov maps

Let $F$ be a (non-Markov) countably piecewise expanding interval map satisfying certain regularity conditions, and $\tildeŁ$ the corresponding transfer operator. We prove the Dolgopyat inequality for the twisted operator $\tildeŁ_s(v) = \tildeŁ_s(e^{sφ}v)$ acting on the space BV of functions of bounded variation, where $φ$ is a piecewise $C^1$ roof function.

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arXiv2016

A renewal scheme for non-uniformly hyperbolic semiflows

We investigate a renewal scheme for non-uniformly hyperbolic semiflows that closely resembles the renewal scheme developed in the discrete time case, in order to obtain sharp estimates for the correlation function. Also, the involved observables are supported on a flow-box of unbounded length. The present abstract setting does not require the use of Markov structure. However, the classes of examples covered here are rather restrictive. In these examples, it is easier to exploit the full force of the method and get optimal results for observables supported on finite length flow-boxes.

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arXiv2016

Operator renewal theory for continuous time dynamical systems with finite and infinite measure

We develop operator renewal theory for flows and apply this to obtain results on mixing and rates of mixing for a large class of finite and infinite measure semiflows. Examples of systems covered by our results include suspensions over parabolic rational maps of the complex plane, and nonuniformly expanding semiflows with indifferent periodic orbits. In the finite measure case, the emphasis is on obtaining sharp rates of decorrelations, extending results of Gouëzel and Sarig from the discrete time setting to continuous time. In the infinite measure case, the primary question is to prove results on mixing itself, extending our results in the discrete time setting. In some cases, we obtain also higher order asymptotics and rates of mixing.

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arXiv2015

Upper and lower bounds for the correlation function via inducing with general return times

For non-uniformly expanding maps inducing with a general return time to Gibbs Markov maps, we provide sufficient conditions for obtaining higher order asymptotics for the correlation function in the infinite measure setting. Along the way, we show that these conditions are sufficient to recover previous results on sharp mixing rates in the finite measure setting for non-Markov maps, but for a larger class of observables. The results are illustrated by (finite and infinite measure preserving) non-Markov intervals maps with an indifferent fixed point.

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arXiv2015

Operator renewal theory and mixing rates for dynamical systems with infinite measure

We develop a theory of operator renewal sequences in the context of infinite ergodic theory. For large classes of dynamical systems preserving an infinite measure, we determine the asymptotic behaviour of iterates $L^n$ of the transfer operator. This was previously an intractable problem. Examples of systems covered by our results include (i) parabolic rational maps of the complex plane and (ii) (not necessarily Markovian) nonuniformly expanding interval maps with indifferent fixed points. In addition, we give a particularly simple proof of pointwise dual ergodicity (asymptotic behaviour of $\sum_{j=1}^nL^j$) for the class of systems under consideration. In certain situations, including Pomeau-Manneville intermittency maps, we obtain higher order expansions for $L^n$ and rates of mixing. Also, we obtain error estimates in the associated Dynkin-Lamperti arcsine laws.

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arXiv2014

Mixing for some non-uniformly hyperbolic systems

In this work we obtain mixing (and in some cases sharp mixing rates) for a reasonable large class of invertible systems preserving an infinite measure. The examples considered here are the invertible analogue of both Markov and non Markov unit interval maps. Moreover, we obtain results on the decay of correlation in the finite case of invertible non Markov maps, which, to our knowledge, were not previously addressed. The present method consists of a combination of the framework of operator renewal theory, as introduced in the context of dynamical systems by Sarig [39], with the framework of function spaces of distributions developed in the recent years along the lines of Blank, Keller and Liverani [9].

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arXiv2014

Mixing for continuous time dynamical systems with infinite measure

We develop operator renewal theory for flows and apply this to infinite ergodic theory. In particular we obtain results on mixing for a large class of infinite measure semiflows. Examples of systems covered by our results include suspensions over parabolic rational maps of the complex plane, and nonuniformly expanding semiflows with indifferent periodic orbits. In some cases, we obtain higher order asymptotics and rates of mixing.

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