33 citations · 133 across the 21 of their papers we have counts for
24 papers
Linear response due to singularities
Wael Bahsoun, Stefano Galatolo
It is well known that a family of tent-like maps with bounded derivatives has no linear response for typical deterministic perturbations changing the value of the turning point. In…
Globally coupled Anosov diffeomorphisms: Statistical properties
Wael Bahsoun, Carlangelo Liverani, Fanni M. Sélley
We study infinite systems of globally coupled Anosov diffeomorphisms with weak coupling strength. Using transfer operators acting on anisotropic Banach spaces, we prove that the co…
Quenched decay of correlations for nonuniformly hyperbolic random maps with an ergodic driving system
José F. Alves, Wael Bahsoun, Marks Ruziboev +1
In this article we study random tower maps driven by an ergodic automorphism. We prove quenched exponential correlations decay for tower maps admitting exponential tails. Our techn…
Map lattices coupled by collisions: hitting time statistics and collisions per lattice unit
Wael Bahsoun, Fanni M. Sélley
We study map lattices coupled by collision and show how perturbations of transfer operators associated with the spatially periodic approximation of the model can be used to extract…
Anosov diffeomorphisms, anisotropic BV spaces and regularity of foliations
Wael Bahsoun, Carlangelo Liverani
Given any smooth Anosov map we construct a Banach space on which the associated transfer operator is quasi-compact. The peculiarity of such a space is that in the case of expanding…
Almost sure rates of mixing for partially hyperbolic attractors
Jose F. Alves, Wael Bahsoun, Marks Ruziboev
We introduce random towers to study almost sure rates of correlation decay for random partially hyperbolic attractors. Using this framework, we obtain abstract results on almost su…
Variance continuity for Lorenz flows
Wael Bahsoun, Ian Melbourne, Marks Ruziboev
The classical Lorenz flow, and any flow which is close to it in the -topology, satisfies a Central Limit Theorem (CLT). We prove that the variance in the CLT varies continuous…
Linear response for random dynamical systems
Wael Bahsoun, Marks Ruziboev, Benoît Saussol
We study for the first time linear response for random compositions of maps, chosen independently according to a distribution $\PP$. We are interested in the following question: ho…
Quenched decay of correlations for slowly mixing systems
Wael Bahsoun, Christopher Bose, Marks Ruziboev
We study random towers that are suitable to analyse the statistics of slowly mixing random systems. We obtain upper bounds on the rate of quenched correlation decay in a general se…
On the statistical stability of Lorenz attractors with a stable foliation
Wael Bahsoun, Marks Ruziboev
We prove statistical stability for a family of Lorenz attractors with a stable foliation.
Linear response in the intermittent family: differentiation in a weighted -norm
Wael Bahsoun, Benoît Saussol
We provide a general framework to study differentiability of SRB measures for one dimensional non-uniformly expanding maps. Our technique is based on inducing the non-uniformly exp…
A Rigorous Computational Approach to Linear Response
Wael Bahsoun, Stefano Galatolo, Isaia Nisoli +1
We present a general setting in which the formula describing the linear response of the physical measure of a perturbed system can be obtained. In this general setting we obtain an…
Mixing rates and limit theorems for random intermittent maps
Wael Bahsoun, Christopher Bose
We study random transformations built from intermittent maps on the unit interval that share a common neutral fixed point. We focus mainly on random selections of Pomeu-Manneville-…
Rigorous approximation of diffusion coefficients for expanding maps
Wael Bahsoun, Stefano Galatolo, Isaia Nisoli +1
We use Ulam's method to provide rigorous approximation of diffusion coefficients for uniformly expanding maps. An algorithm is provided and its implementation is illustrated using…
On Transfer Operators and Maps with Random Holes
Wael Bahsoun, Joerg Schmeling, Sandro Vaienti
We study Markov interval maps with random holes. The holes are not necessarily elements of the Markov partition. Under a suitable, and physically relevant, assumption on the noise,…
Decay of correlation for random intermittent maps
Wael Bahsoun, Christopher Bose, Yuejiao Duan
We study a class of random transformations built over finitely many intermittent maps sharing a common indifferent fixed point. Using a Young-tower technique, we show that the map…
Rigorous pointwise approximations for invariant densities of nonuniformly expanding maps
Wael Bahsoun, Christopher Bose, Yuejiao Duan
We use an Ulam-type discretization scheme to provide pointwise approximations for invariant densities of interval maps with a neutral fixed point. We prove that the approximate inv…
Pseudo-Orbits, Stationary Measures and Metastability
Wael Bahsoun, Huyi Hu, Sandro Vaienti
We study random perturbations of multidimensional piecewise expanding maps. We characterize absolutely continuous stationary measures (acsm) of randomly perturbed dynamical systems…
Escape Rates Formulae and Metastability for Randomly perturbed maps
Wael Bahsoun, Sandro Vaienti
We provide escape rates formulae for piecewise expanding interval maps with `random holes'. Then we obtain rigorous approximations of invariant densities of randomly perturbed meta…
Metastability of Certain Intermittent Maps
Wael Bahsoun, Sandro Vaienti
We study an intermittent map which has exactly two ergodic invariant densities. The densities are supported on two subintervals with a common boundary point. Due to certain perturb…
Invariant densities and escape rates: Rigorous and computable approximations in the -norm
Wael Bahsoun, Christopher Bose
In this article we study a piecewise linear discretization schemes for transfer operators (Perron-Frobenius operators) associated with interval maps. We show how these can be used…
Growth-optimal investments and numeraire portfolios under transaction costs: An analysis based on the von Neumann-Gale model
Wael Bahsoun, Igor V. Evstigneev, Michael I. Taksar
The aim of this work is to extend the capital growth theory developed by Kelly, Breiman, Cover and others to asset market models with transaction costs. We define a natural general…
SRB Measures For Certain Markov Processes
Wael Bahsoun, Pawel Gora
We study Markov processes generated by iterated function systems (IFS). The constituent maps of the IFS are monotonic transformations of the interval. We first obtain an upper boun…
Quasi-Invariant measures, escape rates and the effect of the hole
Wael Bahsoun, Christopher Bose
Let be a piecewise expanding interval map and be an abstract perturbation of into an interval map with a hole. Given a number , , we compute an upper-…