Related papers: Escape rates for Gibbs measures

We consider multimodal maps with holes and study the evolution of the open systems with respect to equilibrium states for both geometric and H\"older potentials. For small holes, we show that a large class of initial distributions share the…

For a fixed initial reference measure, we study the dependence of the escape rate on the hole for a smooth or piecewise smooth hyperbolic map. First, we prove the existence and Holder continuity of the escape rate for systems with small…

The escaping set of an entire function is the set of points that tend to infinity under iteration. We consider subsets of the escaping set defined in terms of escape rates and obtain upper and lower bounds for the Hausdorff measure of these…

We investigate the scaling of the escape rate from piecewise-linear dynamical systems displaying intermittency due to the presence of an indifferent fixed-point. Strong intermittent behaviour in the dynamics can result in the system…

We show that an escape from the potential minimum of Fabry-Perot interferometers can be detected measuring the associated sudden change of reflectivity. We demonstrate that the loss of information that occurs retaining only the sequence of…

We prove an escape rate result for special semi-flows over non-invertible subshifts of finite type. Our proofs are based on a discretisation of the flow and an application of an escape rate result for conformal repellers.

We study non-uniformly expanding maps of the unit interval with a parabolic fixed point at the origin that admit an ergodic absolutely continuous invariant measure, which may be finite or infinite. By introducing a hole defined by an…

We prove sharp asymptotic estimates for the rate of escape of the two-dimensional simple random walk conditioned to avoid a fixed finite set. We derive it from asymptotics available for the continuous analogue of this process (cf…

For a class of non-uniformly hyperbolic interval maps, we study rates of escape with respect to conformal measures associated with a family of geometric potentials. We establish the existence of physically relevant conditionally invariant…

We show that dynamical systems with $\phi$-mixing measures have local escape rates which are exponential with rate $1$ at non-periodic points and equal to the extremal index at periodic points. We apply this result to equilibrium states on…

In this paper escape rates and local escape rates for special flows are sudied. In a general context the first result is that the escape rate depends monotonically on the ceiling function and fulfills certain scaling, invariance, and…

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

Let $1<\beta \leq 2$. It is well-known that the set of points in $% [0,1/(\beta -1)]$ having unique $\beta $-expansion, in other words, those points whose orbits under greedy $\beta $-transformation escape a hole depending on $\beta $, is…

We describe the multifractal nature of random weak Gibbs measures on some class of attractors associated with $C^1$ random dynamics semi-conjugate to a random subshift of finite type. This includes the validity of the multifractal…

We study an asymptotic behaviour of parametric autoresonance for non-linear equation. Main result of this work is statement about asymptotic behaviour of measure for captured trajectories. To find this we obtain an asymptotic expansion for…

In this paper, we analyze the convergence rate of a collapsed Gibbs sampler for crossed random effects models. Our results apply to a substantially larger range of models than previous works, including models that incorporate missingness…

We investigate the escape dynamics of the doubling map with a time-periodic hole. We use Ulam's method to calculate the escape rate as a function of the control parameters. We consider two cases, oscillating or breathing holes, where the…

We prove that for a sequence of nested sets $\{U_n\}$ with $\Lambda = \cap_n U_n$ a measure zero set, the localized escape rate converges to the extremal index of $\Lambda$, provided that the dynamical system is $\phi$-mixing at polynomial…

The escape rate of a stochastic dynamical system can be found as an expansion in powers of the noise strength. In previous work the coefficients of such an expansion for a one-dimensional map were fitted to a general form containing a few…

The study of escape rates for a ball in a dynamical systems has been much studied. Understanding the asymptotic behavior of the escape rate as the radius of the ball tends to zero is an especially subtle problem. In the case of hyperbolic…