Related papers: Effective rates for continuous-time quasi-Fej\'er …
We describe a new continued fraction system in Minkowski space $\mathbb R^{1,1}$, proving convergence, ergodicity with respect to an explicit invariant measure, and Lagrange's theorem. The proof of ergodicity leads us to the question of…
Leveraging the techniques found in the literature on Quantum Equilibration for finite dimensional systems, we develop the theory of Quantum Equilibration for the case of infinite-dimensional systems, particularly the cases where the…
Convergent sequences of real numbers play a fundamental role in many different problems in system theory, e.g., in Lyapunov stability analysis, as well as in optimization theory and computational game theory. In this survey, we provide an…
In this paper, some characterizations about transitivity, mildly mixing property, $\mathbf{a}$-transitivity, equicontinuity, uniform rigidity and proximality of Zadeh's extensions restricted on some invariant closed subsets of the space of…
We investigate convergence properties of discrete-time semigroup quantum dynamics, including asymptotic stability, probability and speed of convergence to pure states and subspaces. These properties are of interest in both the analysis of…
We develop the basics of a theory of almost isometries for spaces endowed with a quasi-metric. The case of non-reversible Finsler (more specifically, Randers) metrics is of particular interest, and it is studied in more detail. The main…
We present a notion of almost periodicity wich can be applied to random dynamical systems as well as almost periodic stochastic differential equations in Hilbert spaces (abstract stochastic partial differential equations). This concept…
We develop and analyze a highly efficient, second-order time-marching scheme for infinite-dimensional nonlinear geophysical fluid models, designed to accurately approximate invariant measures-that is, the stationary statistical properties…
In this work, we consider a continuous dynamical system associated with the fixed point set of a nonexpansive operator which was originally studied by Bo\c{t} & Csetnek (2015). Our main results establish convergence rates for the system's…
A fast convergence in a fixed-time of solutions of nonlinear dynamical systems, for which special requirements are satisfied on the derivative of a quadratic function calculated along the solutions of the system, is proposed. The conditions…
Generalized metric spaces are obtained by weakening the requirements (e.g., symmetry) on the distance function and by allowing it to take values in structures (e.g., quantales) that are more general than the set of non-negative real…
This work proposes block-coordinate fixed point algorithms with applications to nonlinear analysis and optimization in Hilbert spaces. The asymptotic analysis relies on a notion of stochastic quasi-Fej\'er monotonicity, which is thoroughly…
The paper introduces and characterizes new notions of Lipschitzian and H\"olderian full stability of solutions to general parametric variational systems described via partial subdifferential and normal cone mappings acting in Hilbert…
Inspired by group cohomology, we define several coarse topological invariants of metric spaces. We define the coarse cohomological dimension of a metric space, and demonstrate that if G is a countable group, then the coarse cohomological…
In this paper, we investigate the inverse quasi-variational inequality problem in finite-dimensional spaces. First, we introduce a second-order dynamical system whose trajectory converges exponentially to the solution of the inverse…
We consider a class of endomorphisms that contains a set of piecewise partially hyperbolic dynamics semi-conjugated to non-uniformly expanding maps. Our goal is to study a class of endomorphisms that preserve a foliation that is almost…
Sufficiently accurate finite state models, also called symbolic models or discrete abstractions, allow one to apply fully automated methods, originally developed for purely discrete systems, to formally reason about continuous and hybrid…
A compactness of the Revuz map is established in the sense that the locally uniform convergence of a sequence of positive continuous additive functionals is derived in terms of their smooth measures. To this end, we first introduce a metric…
Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in…
This paper is a continuation to the study of generalized quasi contractive operators, essentially due to Akhtar et al. [A multi-step implicit iterative process for common fixed points of generalized C^{q}-operators in convex metric spaces,…