There are numerous physical situations in which a hole or leak is introduced in an otherwise
closed chaotic system. The leak can have a natural origin, it can mimic measurement …

Statistical properties for recurrent and non recurrent escaping particles in an oval billiard
with holes in the boundary are investigated. We determine where to place the holes and …

Most of the existing methods and techniques for the detection of chaotic behaviour from
empirical time series try to quantify the well-known sensitivity to initial conditions through the …

The existence of heteroclinic orbits of a chaotic system is a difficult yet interesting
mathematical problem. Nowadays, a rigorous analytical proof for the existence of a …

We consider one-dimensional discrete-time random walks (RWs) in the presence of finite
size traps of length ℓ over which the RWs can jump. We study the survival probability of such …

We investigate mushroom billiards, a class of dynamical systems with sharply divided phase
space. For typical values of the control parameter of the system ρ, an infinite number of …

We consider escape from chaotic maps through a subset of phase space, the hole. Escape
rates are known to be locally constant functions of the hole position and size. In spite of this …

We determine the analytic expression of the Rayleigh potential associated to the general
relativistic Poynting-Robertson effect. This constitutes the first example of a physical …

We provide escape rates formulae for piecewise expanding interval maps with'random
holes'. Then we obtain rigorous approximations of invariant densities of randomly perturbed …

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 …