Related papers: Exponential Decay of Expansive Constants

We study an asymptotic behaviour of the principal eigenvalue for an elliptic operator with large advection which is given by a gradient of a potential function. It is shown that the principal eigenvalue decays exponentially under the…

We give some natural sufficient conditions for balls in a metric space to have small intersection. Roughly speaking, this happens when the metric space is (i) expanding and (ii) well-spread, and (iii) a certain random variable on the…

In this article, we present a sufficient condition for the exponential $\exp({-f})$ to have a tail decay stronger than any Gaussian, where $f$ is defined on a locally convex space $X$ and grows faster than a squared seminorm on $X$. In…

We establish upper bounds for the decay rate of the energy of the damped fractional wave equation when the averages of the damping coefficient on all intervals of a fixed length are bounded below. If the power of the fractional Laplacian,…

Under a map T, a point x recurs at rate given by a sequence {r_n} near a point x_0 if d(T^n(x),x_0)< r_n infinitely often. Let us fix x_0, and consider the set of those x's. In this paper, we study the size of this set for expanding maps…

We study the elusive transition from exponential to post-exponential (algebraic) decay of the probability density of a quantum particle emitted by an exponentially decaying source, in one dimension. The main finding is that the probability…

We study the one-dimensional expanding Lorenz maps and show the existence of dense subset D of Lorens maps such that each f in D has an uncountable set of ergodic invariant probabilities with infinite Lyapunov exponent and positive entropy.…

We consider random perturbations of non-uniformly expanding maps, possibly having a non-degenerate critical set. We prove that, if the Lebesgue measure of the set of points failing the non-uniform expansion or the slow recurrence to the…

We give an upper bound for the topological entropy of maps on inverse limit spaces in terms of their set-valued components. In a special case of a diagonal map on the inverse limit space $\underleftarrow{\lim}(I,f)$, where every diagonal…

We consider the problem of constructing a weakly-continuous mapping extending continuous mapping defined on a dense set of a topological space to the entire space. Theorem on necessary and sufficient conditions for the existence of such an…

This paper discusses possible approaches to the escape rate in infinite lattices of weakly coupled maps with uniformly expanding repeller. It is proved that computed-via-volume rates of spatially periodic approximations grow linearly with…

The expansion exponent (or expansion constant) for maps was introduced by Schreiber in \cite{s}. In this paper, we introduce the analogous exponent for measures. We shall prove the following results: The expansion exponent of a measurable…

In this paper, we study the non-self dual extended Harper's model with Liouvillean frequency. By establishing quantitative reducibility results together with the averaging method, we prove that the lengths of spectral gaps decay…

How can we interpret the infimum of Lipschitz constants in a conjugacy class of interval maps? For positive entropy maps, the exponential of the topological entropy gives a well-known lower bound. We show that for piecewise monotone…

Let $f$ be a $C^{1}$ diffeomorphism on a compact manifold $M$ admitting a partially hyperbolic splitting $TM=E^{s}\oplus_{\prec} E^{1}\oplus_{\prec} E^{2}\cdots \oplus_{\prec}E^{l}\oplus_{\prec} E^{u}$ where $E^{s}$ is uniformly…

For first order systems, we obtain an efficient bound on the exponential decay of an eigenfunction in terms of the distance between the corresponding eigenvalue and the essential spectrum. As an example, the Dirac operator is considered.

We have investigated the random walk problem in a finite system and studied the crossover induced in the the persistence probability scales by the system size.Analytical and numerical work show that the scaling function is an exponentially…

We study the exponential decay of relative entropy functionals for zero-range processes on the complete graph. For the standard model with rates increasing at infinity we prove entropy dissipation estimates, uniformly over the number of…

We consider the transmission problem for a coupled system of undamped and structurally damped plate equations in two sufficiently smooth and bounded subdomains. It is shown that, independently of the size of the damped part, the damping is…

In the context of expanding maps of the circle with an indifferent fixed point, understanding the joint behavior of dynamics and pairs of moduli of continuity $ (\omega, \Omega) $ may be a useful element for the development of equilibrium…