Related papers: Flexibility of generalized entropy for wandering d…
We show how geometric methods from the general theory of fractal dimensions and iterated function systems can be deployed to study symbolic dynamics in the zero entropy regime. More precisely, we establish a dimensional characterization of…
We compute for an archetypical glass-forming system the excess of particle mobility distributions over the corresponding distribution of dynamic propensity, a quantity that measures the tendency of the particles to be mobile and reflects…
The aim of the present paper is to study conditions under which all the non-wandering points are periodic points, for a discrete dynamical system of two variables defined on a compact manifold. We include a survey of known results in all…
The notion of $\Delta$-weakly mixing set is introduced, which shares similar properties of weakly mixing sets. It is shown that if a dynamical system has positive topological entropy, then the collection of $\Delta$-weakly mixing sets is…
We address in this paper how tightly the composability nature of systems: $S_{A+B} =\Omega (S_A, S_B)$ constrains definition of generalized entropies and investigate explicitly the composability in some ansatz of the entropy form.
Topological entropy is not lower semi-continous: small perturbation of the dynamical system can lead to a collapse of entropy. In this note we show that for some special classes of dynamical systems (geodesic flows, Reeb flows, positive…
This article presents a general description of dynamical systems using the language of enriched functors and enriched natural transformations. This framework is essential to establish the equivalence of three descriptions of dynamics -- a…
We provide a quantum statistical basis for (a)a characterisation of a complete set of thermodynamic variables and (b) the differentiability of the entropy function of these variables
We present results for the equilibrium statistics and dynamic evolution of moderately large ($n = {\mathcal{O}}(10^2 - 10^3)$) numbers of interacting point vortices on the unit sphere under the constraint of zero mean angular momentum. We…
Entanglement and stabilizer entropy are both involved in the onset of complex behavior in quantum many-body systems. Their interplay is at the root of complexity of simulability, scrambling, thermalization and typicality. In this work, we…
We investigate the quintessence scalar field model modified by the Generalized Uncertainty Principle in the background of a spatially flat homogeneous and isotropic universe. By performing a dynamical system analysis we examine the nature…
Fluid dynamics corresponds to the dynamics of a substance in the long wavelength limit. Writing down all terms in a gradient (long wavelength) expansion up to second order for a relativistic system at vanishing charge density, one obtains…
We present a dichotomy for surface homeomorphisms in the isotopy class of the identity. We show that, in the absence of a degenerate fixed point set, either there exists a uniform bound on the diameter of orbits of non-wandering points for…
In [30] different statistical behavior of dynamical orbits without syndetic center are considered. In present paper we continue this project and consider different statistical behavior of dynamical orbits with nonempty syndetic center: Two…
Here we present the entropic dynamics formalism for networks. That is, a framework for the dynamics of graphs meant to represent a network derived from the principle of maximum entropy and the rate of transition is obtained taking into…
We study the problem of detecting the structure of a complex dynamical system described by a set of deterministic differential equation that contains a Hamiltonian subsystem, without any information on the explicit form of evolution laws.…
We consider some local entropy properties of dynamical systems under the assumption of shadowing. In the first part, we give necessary and sufficient conditions for shadowable points to be certain entropy points. In the second part, we give…
Glasses are ubiquitous amorphous solids that remain one of the big mysteries in condensed matter. Despite the vast body of literature on glasses, a unifying approach to link the structure and dynamics of glasses is still missing. A growing…
In this article we construct an expansive homeomorphism of a compact three-dimensional manifold with a fixed point whose local stable set is not locally connected. This homeomorphism is obtained as a topological perturbation of a…
We study the slippage of a gas along mobile rigid walls in the sphere-plane confined geometry and find that it varies considerably with pressure. The classical no-slip boundary condition valid at ambient pressure changes continuously to an…