Related papers: Slow escape in tracts
Let $f$ be a piecewise continuous and monotonic map on the interval with at most finitely many discontinuities and turning points. In this paper we study properties about this class of maps and show its main difference from the continuous…
We consider convex hulls of random walks whose steps belong to the domain of attraction of a stable law in $\mathbb{R}^d$. We prove convergence of the convex hull in the space of all convex and compact subsets of $\mathbb{R}^d$, equipped…
An existence theorem for stationary discs of strongly pseudoconvex domains in almost complex manifolds is proved. More precisely, it is shown that, for all points of a suitable neighborhood of the boundary and for any vector belonging to…
We establish vanishing results for limits of characters in various discrete groups, most notably irreducible lattices in higher rank semisimple Lie groups. As an application, we show that any sequence of finite-dimensional representations…
Global existence of weak solutions to the Navier-Stokes equation in a cylindrical domain under the slip boundary conditions and with inflow and outflow was proved. To prove the energy estimate, crucial for the proof, we use the Hopf…
We study the computational complexity of the Escape Problem for discrete-time linear dynamical systems over compact semialgebraic sets, or equivalently the Termination Problem for affine loops with compact semialgebraic guard sets. Consider…
Consider the time T_oz when the random walk on a weighted graph started at the vertex o first hits the vertex set z. We present lower bounds for T_oz in terms of the volume of z and the graph distance between o and z. The bounds are for…
A critical review of experimental studies of the so-called 'slow light' arising due to anomalously high steepness of the refractive index dispersion under conditions of electromagnetically induced transparency or coherent population…
We show that the points that converge to infinity under iteration of the exponential map form a connected subset of the complex plane.
We consider Reeb flows on the tight $3$-sphere admitting a pair of closed orbits forming a Hopf link. If the rotation numbers associated to the transverse linearized dynamics at these orbits fail to satisfy a certain resonance condition…
Adsorption to a surface, reversible-binding, and trapping are all prevalent scenarios where particles exhibit "stickiness". Escape and first-passage times are known to be drastically affected, but detailed understanding of this phenomenon…
The transit method is a promising means to detect exomoons, but few candidates have been identified. For planets close to their stars, the dynamical interaction between a satellite's orbit and the star must be important in their evolution.…
We consider reversible random walks in random environment obtained from symmetric long--range jump rates on a random point process. We prove almost sure transience and recurrence results under suitable assumptions on the point process and…
In this paper, we consider a subshift of finite type with Markov measure. By considering a union of cylinders as holes, we investigate the exponential growth rate of measure of points whose orbits do not escape into the hole over a fixed…
We impose standard $ T1 $-type assumptions on a Calder\'on-Zygmund operator $ T $, and deduce that for bounded compactly supported functions $ f, g $ there is a sparse bilinear form $ \Lambda $ so that $$ \lvert \langle T f, g \rangle\rvert…
For small $\epsilon>0$, the system $\dot x = \epsilon$, $\dot z = h(x,z,\epsilon)z$, with $h(x,0,0)<0$ for $x<0$ and $h(x,0,0)>0$ for $x>0$, admits solutions that approach the $x$-axis while $x<0$ and are repelled from it when $x>0$. The…
Functors with an instance of the Traversable type class can be thought of as data structures which permit a traversal of their elements. This has been made precise by the correspondence between traversable functors and finitary containers…
We establish a deterministic technique to investigate transport moments of arbitrary order. The theory is applied to the analysis of different kinds of intermittent one-dimensional maps and the Lorentz gas with infinite horizon: the typical…
Semiclassical behavior of Stark resonances is studied. The complex distortion outside a cone is introduced to study resonances in any energy region for the Stark Hamiltonians with non-globally analytic potentials. The non-trapping resolvent…
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.