Related papers: Inheritance of shadowing for dynamical semigroups
The semiring of discrete dynamical systems is a simple algebraic model for modularity in deterministic systems. The objects of the semiring are finite transformations (viewed as directed graphs and regarded up to isomorphism), the sum of…
In an attempt to propose more general conditions for decoherence to occur, we study spectral and ergodic properties of unital, completely positive maps on not necessarily unital $C^*$-algebras, with a particular focus on gapped maps for…
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 study invariant theory of the general linear supergroup in positive characteristic. In particular, we determine when the symmetric group algebra acts faithfully on tensor superspace and demonstrate that the symmetric group does not…
Isoperimetric inequalities have been studied since antiquity, and in recent decades they have been studied extensively on discrete objects, such as the hypercube. An important special case of this problem involves bounding the size of the…
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…
A description of the endomorphisms of semidirect products of two groups as a group of $2\times 2$ matrices of maps is already known. Using this description, we have studied the concept of determinant for the endomorphisms of semidirect…
We introduce shadow structures for singular knot theory. Precisely, we define \emph{two} invariants of singular knots and links. First, we introduce a notion of action of a singquandle on a set to define a shadow counting invariant of…
This paper is a contribution to the theory of finite semigroups and their classification in pseudovarieties, which is motivated by its connections with computer science. The question addressed is what role can play the consideration of an…
In this paper we discuss graph inverse semigroups which are constucted from a directed graphs and study several interesting properties of graph inverse semigroups such as the nature of its idempotents, the structure of semilattice of…
We describe a construction of cocyclic perturbations of the semigroup of shifts on the semiaxis by means of the theory of model spaces. It is shown that one can choose an inner function that determines the model space so that the elements…
We prove that given a fixed finite tree $P$, almost all trees contain $P$ as a subtree. Moreover, the inclusion can be made so that it induces an embedding of the corresponding (quantum) automorphism groups, thereby providing generic…
We consider quantum walks on a finite graphs to which infinite tails are attached. We explore how the propagating and bound states depend on the structure of the finite graph. The S-matrix for such graphs is defined. Its unitarity is proved…
We characterise the respective semigroups of mappings that preserve, or that preserve or reverse orientation of a finite cycle, in terms of their actions on oriented triples and oriented quadruples. This leads to a proof that the latter…
Recently it was proved that the group of rough paths modulo tree-like equivalence is isomorphic to the corresponding signature group through the signature map S (a generalized notion of taking iterated path integrals). However, the proof of…
In general, intrinsic image decomposition algorithms interpret shading as one unified component including all photometric effects. As shading transitions are generally smoother than reflectance (albedo) changes, these methods may fail in…
The notion \emph{Perron-Frobenius theory} usually refers to the interaction between three properties of operator semigroups: positivity, spectrum and long-time behaviour. These interactions gives rise to a profound theory with plenty of…
Utilizing concepts from dynamical systems theory, we demonstrate how the existence of light rings, or fixed points, in a spacetime will give rise to families of periodic orbits and invariant manifolds in phase space. It is shown that these…
Machine learning methods can be unreliable when deployed in domains that differ from the domains on which they were trained. There are a wide range of proposals for mitigating this problem by learning representations that are ``invariant''…
Due to the Heisenberg uncertainty principle, various classical systems differing only on the scale smaller than Planck's cell correspond to the same quantum system. This fact is used to find a unique semiclassical representation without the…