Related papers: Entry times distribution for dynamical balls on me…
Previously it has been shown that some classes of mixing dynamical systems have limiting return times distributions that are almost everywhere Poissonian. Here we study the behaviour of return times at periodic points and show that the…
We prove that multimodal maps with an absolutely continuous invariant measure have exponential return time statistics around a.e. point. We also show a `polynomial Gibbs property' for these systems, and that the convergence to the entropy…
This paper addresses a class of impulsive systems defined by a mix of continuous-time and discrete-time switched linear dynamics. We first analyze a related class of weighted discrete-time switched systems for which we establish a…
The probability distribution for multiple collisions observed in the chaotic low energy domain in the bouncing ball model is shown to be scaling invariant concerning the control parameters. The model considers the dynamics of a bouncing…
We call a system bouncing ball billiard if it consists of a particle that is subjected to a constant vertical force and bounces inelastically on a one-dimendional vibrating periodically corrugated floor. Here we choose circular scatterers…
We study the number of visits to balls B_r(x), up to time t/mu(B_r(x)), for a class of non-uniformly hyperbolic dynamical systems, where mu is the SRB measure. Outside a set of `bad' centers x, we prove that this number is approximately…
We study from a statistical physics perspective the dynamics of a bouncing ball maintained in a chaotic regime thanks to collisions with a plate experiencing an aperiodic vibration. We analyze in details the energy exchanges between the…
Dynamical systems having many coexisting attractors present interesting properties from both fundamental theoretical and modelling points of view. When such dynamics is under bounded random perturbations, the basins of attraction are no…
We analyze, both analytically and numerically, the time-dependence of the return probability in closed systems of interacting particles. Main attention is paid to the interplay between two regimes, one of which is characterized by the…
We prove that random walks in random environments, that are exponentially mixing in space and time, are almost surely diffusive, in the sense that their scaling limit is given by the Wiener measure.
We cosider random dynamical systems with randomly chosen jumps. The choice of deterministic dynamical system and jumps depends on a position. We proove the existence of an exponentially attractive invariant measure and the strong law of…
We construct various novel and elementary examples of dynamics with metric attractors that have intermingled basins. A main ingredient is the introduction of random walks along orbits of a given dynamical system. We develop theory for it…
Motion of particles in many systems exhibits a mixture between periods of random diffusive like events and ballistic like motion. In many cases, such systems exhibit strong anomalous diffusion, where low order moments $< |x(t)|^q >$ with…
We show in detail some results, outlined in a previous paper regarding the case of Brownian motion (BM), about the distribution of the $n$th-passage time of a one-dimensional diffusion obtained by a space or time transformation of BM,…
We study analytically the dynamics of a ball bouncing inelastically on a randomly vibrating platform, as a simple toy model of inelastic collapse. Of principal interest are the distributions of the number of flights n_f till the collapse…
The L\'evy walk process with rests is discussed. The jumping time is governed by an $\alpha$-stable distribution with $\alpha>1$ while a waiting time distribution is Poissonian and involves a position-dependent rate which reflects a…
We consider discrete time dynamical systems and show the link between Hitting Time Statistics (the distribution of the first time points land in asymptotically small sets) and Extreme Value Theory (distribution properties of the partial…
We consider the vertical motion of a free falling ball bouncing elastically on a racket moving in the vertical direction according to a regular periodic function $f$. We give a sufficient condition on the second derivative of $f$ giving…
We derive diffusion constants and martingales for senile random walks with the help of a time-change. We provide direct computations of the diffusion constants for the time-changed walks. Alternatively, the values of these constants can be…
We consider the model describing the vertical motion of a ball falling with constant acceleration on a wall and elastically reflected. The wall is supposed to move in the vertical direction according to a given periodic function $f$. We…