Related papers: A Rigorous Computational Approach to Linear Respon…
We present a rigorous numerical scheme for the approximation of the linear response of the invariant density of a map with an indifferent fixed point, with explicit and computed estimates for the error and all the involved constants.
We show a linear response statement for fixed points of a family of Markov operators which are perturbations of mixing and regularizing operators. We apply the statement to random dynamical systems on the interval given by a deterministic…
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 expanding system to a uniformly expanding one, and on showing…
How can one change a system, in order to change its statistical properties in a prescribed way? In this note we consider a control problem related to the theory of linear response. Given an expanding map of the unit circle with an…
Linear Response theory aims to predict how added forcing alters the statistical properties of an unforced system. These kinds of questions have been studied predominantly for autonomous dynamical systems, yet many systems in the physical,…
We prove ``effective'' linear response for certain classes of non-uniformly expanding random dynamical systems which are not necessarily composed in an i.i.d manner. In applications, the results are obtained for base maps with a sufficient…
We consider discontinuous perturbations of smooth endomorphisms and show that if the perturbed family satisfies uniform mixing assumptions on standard pairs the physical measure is Lipschitz in the parameter defying the perturbation. We…
Using equilibrium fluctuations to understand the response of a physical system to an externally imposed perturbation is the basis for linear response theory, which is widely used to interpret experiments and shed light on microscopic…
The linear response of synchronized chaotic units with delayed couplings and feedback to small external perturbations is investigated in the context of communication with chaos synchronization. For iterated chaotic maps, the distribution of…
We consider controllable linear discrete-time systems with bounded perturbations and present two methods to compute robust controlled invariant sets. The first method tolerates an arbitrarily small constraint violation to compute an…
This work establishes a quenched (trajectory-wise) linear response formula for random intermittent dynamical systems, consisting of Liverani-Saussol-Vaienti maps with varying parameters. This result complements recent annealed (averaged)…
We develop a family of reformulations of an arbitrary consistent linear system into a stochastic problem. The reformulations are governed by two user-defined parameters: a positive definite matrix defining a norm, and an arbitrary discrete…
We consider the linear and quadratic higher order terms associated to the response of the statistical properties of a dynamical system to suitable small perturbations. These terms are related to the first and second derivative of the…
We define the complexity of a continuous-time linear system to be the minimum number of bits required to describe its forward increments to a desired level of fidelity, and compute this quantity using the rate distortion function of a…
Understanding how systems respond to external perturbations is fundamental to statistical physics. For systems far from equilibrium, a general framework for response remains elusive. While progress has been made on the linear response of…
We study a system of all-to-all weakly coupled uniformly expanding circle maps in the thermodynamic limit. The state of the system is described by a probability measure and its evolution is given by the action of a nonlinear operator, also…
We describe a framework in which is possible to develop and implement algorithms for the approximation of invariant measures of dynamical systems with a given bound on the error of the approximation. Our approach is based on a general…
In this note we consider a tent-like family with a cusp at the singular point and show that the linear response holds for certain perturbations of this family. This contrasts the tent-like maps with finite derivatives at the singularity.…
This paper addresses the classical problem of determining the sets of possible states of a linear discrete-time system subject to bounded disturbances from measurements corrupted by bounded noise. These so-called uncertainty sets evolve…
The linear response of synchronized time-delayed chaotic systems to small external perturbations, i.e., the phenomenon of chaos pass filter, is investigated for iterated maps. The distribution of distances, i.e., the deviations between two…