Related papers: Average shadowing and gluing property

The character theory of finite groups has numerous basic questions that are often already quite involved: enumerating of irreducible characters, their character formulas, point-wise product decompositions, and restriction/induction between…

We offer a solution to a long-standing problem in the physics of networks, the creation of a plausible, solvable model of a network that displays clustering or transitivity -- the propensity for two neighbors of a network node also to be…

Grating spectra exhibit sharp variations of the scattered light, known as grating anomalies. The latter are due to resonances that have fascinated specialists of optics and physics for decades and are nowadays used in many applications. We…

We consider low-dimensional systems with the shadowing property. In dimension two, we show that the shadowing property for a homeomorphism implies the existence of periodic orbits in every $\epsilon$-transitive class, and in contrast we…

Supersymmetric states in M-theory are mapped after compactification to perturbatively non-supersymmetric states in type IIA string theory, with the supersymmetric parts being encoded in the non-perturbative section of the string theory. An…

We establish a general `gluing theorem', which states roughly that if two nondegenerate constant mean curvature surfaces are juxtaposed, so that their tangent planes are parallel and very close to one another, but oppositely oriented, then…

We study three notions of shadowing: classical shadowing, limit (or asymptotic) shadowing, and s-limit shadowing. We show that classical and s-limit shadowing coincide for tent maps and, more generally, for piecewise linear interval maps…

We prove that for finitely generated free semigroup actions the average shadowing property, the weak asymptotic average shadowing property, the mean ergodic shadowing property, the almost asymptotic average shadowing property, the…

In this paper, we study stochastic stability of a dynamical system with shadowing property, which evolves under small random perturbation. We prove that time averages along the pseudo-trajectory converge with respect to stationary measure…

We introduce a general notion of covering property, of which many classical definitions are particular instances. Notions of closure under various sorts of convergence, or, more generally, under taking kinds of accumulation points, are…

Feature Learning aims to extract relevant information contained in data sets in an automated fashion. It is driving force behind the current deep learning trend, a set of methods that have had widespread empirical success. What is lacking…

We show that both abelian and non-abelian gauge theories admit configurations in which the fields behave as if in the presence of static charge densities, or ``shadow charges". These correspond to nontrivial initial conditions for the…

Phase gradient metagratings/metasurfaces (PGMs) have provided a new paradigm for light manipulations. In this work, we will show the existence of gauge invariance in PGMs, i.e., the diffraction law of PGMs is independent of the choice of…

The phenomenon of shadowing of nuclear structure functions at small values of Bjorken-$x$ is analyzed. First, multiple scattering is discussed as the underlying physical mechanism. In this context three different but related approaches are…

We generalize two classical results of Maizel and Pliss that describe relations between hyperbolicity properties of linear system of difference equations and its ability to have a bounded solution for every bounded inhomogeneity. We also…

This paper proves that shadowing solutions can be almost surely nonphysical. This finding invalidates the argument that small perturbations in a chaotic system can only have a small impact on its statistical behavior. This theoretical…

We make two improvements upon Joyce's gluing theorems of for compact special Lagrangian submanifolds with isolated conical singularities. Firstly, we get rid of a few technical hypotheses of them. Secondly, we replace another hypothesis by…

The article continues the study of the 'regular' arrangement of a collection of sets near a point in their intersection. Such regular intersection or, in other words, transversality properties are crucial for the validity of qualification…

Perturbative superstring theory is revisited, with the goal of giving a simpler and more direct demonstration that multi-loop amplitudes are gauge-invariant (apart from known anomalies), satisfy space-time supersymmetry when expected, and…

We introduce three forms of generalized contraction (GC). Roughly speaking, these are motivated by allowing contraction to take place after small transients in time and/or amplitude. Indeed, contraction is usually used to prove asymptotic…