Related papers: Amorphic complexity
A sofic approximation to a countable group is a sequence of partial actions on finite sets that asymptotically approximates the action of the group on itself by left-translations. A group is sofic if it admits a sofic approximation. Sofic…
We present a new asymptotic strategy for general micro-macro models which analyze complex viscoelastic fluids governed by coupled multiscale dynamics. In such models, the elastic stress appearing in the macroscopic continuum equation is…
We introduce the group-compact coarse structure on a Hausdorff topological group in the context of coarse structures on an abstract group which are compatible with the group operations. We develop asymptotic dimension theory for the…
In this paper we apply techniques from nonstandard analysis to study expansive dynamical systems. Among other results, we provide a necessary and sufficient condition for an expansive homeomorphism on a compact metric space to admit…
We study the computational problem of rigorously describing the asymptotic behaviour of topological dynamical systems up to a finite but arbitrarily small pre-specified error. More precisely, we consider the limit set of a typical orbit,…
We discuss the dependence of set-valued dynamical systems on parameters. Under mild assumptions which are often satisfied for random dynamical systems with bounded noise and control systems, we establish the fact that topological…
Different notions of entropy play a fundamental role in the classical theory of dynamical systems. Unlike many other concepts used to analyze autonomous dynamics, both measure-theoretic and topological entropy can be extended quite…
We study nontrivial entropy invariants in the class of parabolic flows on homogeneous spaces, quasi-unipotent flows. We show that topological complexity (ie, slow entropy) can be computed directly from the Jordan block structure of the…
The aim of this note is to introduce a notion of dynamical entropy, which we call infinite-product entropy, for probability measures on (countable) infinite cartesian product of any measurable space with itself. The idea behind the…
Complexity of two-level systems, e.g. spins, qubits, magnetic moments etc, are analysed based on the so-called correlational entropy in the case of pure quantum systems and the thermal entropy in case of thermal equilibrium that are…
During the last years, asymptotic (or sequential) constraint qualifications, which postulate upper semicontinuity of certain set-valued mappings and provide a natural companion of asymptotic stationarity conditions, have been shown to be…
Asymptotic almost automorphy is introduced and studied in the context of some algebras of generalized functions. We also give applications to neutral difference differential systems in the framework of such generalized functions.
We investigate the role of entropic concepts for the relaxation dynamics in granular systems. In these systems the existence of a geometrical frustration induces a drastic modification of the allowed phase space, which in its turn induces a…
We define a hierarchy of systems with topological completely positive entropy in the context of continuous countable amenable group actions on compact metric spaces. For each countable ordinal we construct a dynamical system on the…
We define correlational (von Neumann) entropy for an individual quantum state of a system whose time-independent hamiltonian contains random parameters and is treated as a member of a statistical ensemble. This entropy is representation…
Some problems in the theory and applications of stochastic processes can be reduced to solving integral equations. While explicit solutions for these equations are often elusive, valuable insights can be gained through their asymptotic…
In this review we establish various connections between complex networks and symmetry. While special types of symmetries (e.g., automorphisms) are studied in detail within discrete mathematics for particular classes of deterministic graphs,…
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…
Complex networks are a successful framework to describe collective behaviour in many applications, but a notable gap remains in the current literature, that of proving asymptotic convergence in networks of piecewise-smooth systems. Indeed,…
The topological structure of basin boundaries plays a fundamental role in the sensitivity to the initial conditions in chaotic dynamical systems. Herewith we present a study on the dynamics of dissipative systems close to the Hamiltonian…