Related papers: Topological Transitivity of Nonautonomous Dynamica…

The thesis presents the subject of synthetic topology, especially with relation to metric spaces. A model of synthetic topology is a categorical model in which objects possess an intrinsic topology in a suitable sense, and all morphisms are…

The interplay between unitary dynamics and quantum measurements induces diverse phenomena in open quantum systems with no counterparts in closed quantum systems at equilibrium. Here, we generally classify Kraus operators and their effective…

Dynamical systems theory is especially well-suited for determining the possible asymptotic states (at both early and late times) of cosmological models, particularly when the governing equations are a finite system of autonomous ordinary…

Discrete quantum walks are dynamical protocols for controlling a single quantum particle. Despite of its simplicity, quantum walks display rich topological phenomena and provide one of the simplest systems to study and understand…

The dynamical and topological properties of non-Hermitian systems have attracted great attention in recent years. In this work, we establish an intrinsic connection between two classes of intriguing phenomena -- topological phases and…

Topology and nonlinearity are deeply connected. However, whether topological effects can arise solely from the structure of nonlinear interaction terms, and the nature of the resulting topological phases, remain to large extent open…

In this paper, we present a unifying analytical framework for identifying conditions for transport effects such as reflectionless and transparent transport, lasing, and coherent perfect absorption in non-Hermitian nonreciprocal systems…

Connectedness, path connectedness, and uniform connectedness are well-known concepts. In the traditional presentation of these concepts there is a substantial difference between connectedness and the other two notions, namely connectedness…

A contractive condition is addressed for extended 2-cyclic self-mappings on the union of a finite number of subsets of a metric space which are allowed to have a finite number of successive images in the same subsets of its domain. It is…

As the motions of nonconservative autonomous systems are typically not periodic, the definition of nonlinear modes as periodic motions cannot be applied in the classical sense. In this paper, it is proposed 'make the motions periodic' by…

Covering relations are a topological tool for detecting periodic orbits, symbolic dynamics and chaotic behavior for autonomous ODE. We extend the method of the covering relations onto systems with a time dependent perturbation. As an…

Non-Hermitian singularities are ubiquitous in non-conservative open systems. These singularities are often points of measure zero in the eigenspectrum of the system which make them difficult to access without careful engineering. Despite…

We consider integrable Hamiltonian systems in a general setting of invariant submanifolds which need not be compact. For instance, this is the case a global Kepler system, non-autonomous integrable Hamiltonian systems and integrable systems…

We give a new definition of topological pressure for arbitrary (non-compact, non-invariant) Borel subsets of metric spaces. This new quantity is defined via a suitable variational principle, leading to an alternative definition of an…

This work proposes to model the space environment as a stochastic dynamic network where each node is a group of objects of a given class, or species, and their relationship is represented by stochastic links. A set of stochastic dynamic…

The current paper is devoted to the investigation of the influence of nested invariant cone structure on the dynamics, in the context of non-autonomous (time almost periodic)cases. We first prove that the nested invariant cone structure can…

We show that non-Hermiticity enables topological phases with unidirectional transport in one-dimensional Floquet chains. The topological signatures of these phases are non-contractible loops in the spectrum of the Floquet propagator that…

Transition out of a topological phase is typically characterized by discontinuous changes in topological invariants along with bulk gap closings. However, as a clean system is geometrically punctured, it is natural to ask the fate of an…

Distributive subsets of the group of all invertible continuous binary operations on a topological space are considered, and it is proved that the subgroups generated by them are also distributive. A criterion for the distributivity of a…

In this paper, we consider chaotic dynamics and variational structures of area-preserving maps. There is a lot of study on dynamics of their maps and the works of Poincare and Birkhoff are well-known. To consider variational structures of…