Related papers: Shadowing in linear skew products
We consider the problem of testing the identity of a reversible Markov chain against a reference from a single trajectory of observations. Employing the recently introduced notion of a lumping-congruent Markov embedding, we show that, at…
Transitions between steady dynamical regimes in diverse applications are often modelled using discontinuities, but doing so introduces problems of uniqueness. No matter how quickly a transition occurs, its inner workings can affect the…
We use Lyapunov type functions to give new conditions under which a homeomorphism of a compact metric space has the shadowing property. These conditions are applied to establish the topological stability of some homeomorphisms with…
Let {X_n,n\geq0} be a Markov chain on a general state space X with transition probability P and stationary probability \pi. Suppose an additive component S_n takes values in the real line R and is adjoined to the chain such that…
We consider the dimer model on the square and hexagonal lattices with doubly periodic weights. The purpose of this paper is threefold: (a) we establish a rigourous connection with the massive SLE$_2$ constructed by Makarov and Smirnov (and…
Capturing the image of the shadow cast by the event horizon of an illuminated black hole is, at the most basic level, an experiment of extreme light deflection in a strongly curved spacetime. As such, the properties of an imaged shadow can…
We investigate relations between the pseudo-orbit-tracing property, topological stability and openness for tree-shifts. We prove that a tree-shift is of finite type if and only if it has the pseudo-orbit-tracing property which implies that…
The subject is parametrices for semi-linear problems, based on parametrices for linear boundary problems and on non-linearities that decompose into solution-dependent linear operators acting on the solutions. Non-linearities of product type…
We introduce the notion of conditional Lipschitz shadowing, which does not aim to shadow every pseudo-orbit, but only those which belong to a certain prescribed set. We establish two types of sufficient conditions under which certain…
We study the Bernoulli property for skew products with hyperbolic diffeomorphisms equipped with a Gibbs measure in the base and Kochergin flows in the fiber, when the cocycle is aperiodic and of zero mean. The flow in the fiber can be…
The possibility of making an optically large (many wavelengths in diameter) object appear invisible has been a subject of many recent studies. Exact invisibility scenarios for large (relative to the wavelength) objects involve…
We describe the dynamical formation of the shadow of a collapsing star in a Hayward spacetime in terms of an observer far away from the center and a free falling observer. By solving the time-like and light-like radial geodesics we…
We consider a model of loop-erased random walks on the finite pre-Sierpinski gasket which permits rigorous analysis. We prove the existence of the scaling limit and show that the path of the limiting process is almost surely self-avoiding,…
On a weakly Blackwell space we show how to define a Markov chain approximating problem, for the target problem. The approximating problem is proved to converge to the optimal reduced problem under different pseudometrics. A computational…
In many real-world applications data come as discrete metric spaces sampled around 1-dimensional filamentary structures that can be seen as metric graphs. In this paper we address the metric reconstruction problem of such filamentary…
In this paper we present a unified picture concerning Lie-Trotter method for solving a large class of semilinear problems: nonlinear Schr\"odinger, Schr\"oginger--Poisson, Gross--Pitaevskii, etc. This picture includes more general schemes…
Ordinary differential equation (ODE) models of gradient-based optimization methods can provide insights into the dynamics of learning and inspire the design of new algorithms. Unfortunately, this thought-provoking perspective is weakened by…
Let $\Gamma$ be a countable group acting on a geodesic Gromov-hyperbolic metric space $X$ and $\mu$ a probability measure on $\Gamma$ whose support generates a non-elementary subsemigroup. Under the assumption that $\mu$ has a finite…
Sums of lognormal random variables (RVs) occur in many important problems in wireless communications especially in interferences calculation. Several methods have been proposed to approximate the lognormal sum distribution. Most of them…
Recent work suggests unstable recurrent solutions of the equations governing fluid flow can play an important role in structuring the dynamics of turbulence. Here we present a method for detecting intervals of time where turbulence…