in this paper by use of mathematical modeling of an observer [14,15] the notion of relative information functional for relative dynamical systemson compact metric spaces is presented. we extract the information function ofan ergodic dynamical system (x,t) from the relative information of t fromthe view point of observer χx, where x denotes the base space of the system.we also generalize the inv...

We examine the problem of damage spreading in the off-equilibrium mode coupling equations. This study is conducted for the spherical p-spin model introduced by Crisanti, Horner and Sommers. For p > 2 we show the existence of a temperature transition T0 well above any relevant thermodynamic transition temperature. Above T0 the asymptotic damage decays to zero while below T0 it decays to a finite...

In the 19th century the American mathematician G.W. Hill devised a simple and useful approximation for the motion of the moon around the earth with perturbations by the sun. To most dynamical astronomers “Hill’s Problem” still means a model for motions in the solar system in which two nearby bodies move in nearly circular orbits about another much larger body at a great distance. These lectures...

We investigate the incremental stability properties of Itô stochastic dynamical systems. Specifically, we derive a stochastic version of nonlinear contraction theory that provides a bound on the mean square distance between any two trajectories of a stochastically contracting system. This bound can be expressed as a function of the noise intensity and the contraction rate of the noise-free syst...

We consider rapidly mixing dynamical systems and link the decay of shortest distance between multiple orbits with generalized fractal dimension. apply this result to multidimensional expanding maps extend it realm random systems. For sequences, we obtain a relation longest common substring sequences Rényi entropy. Applications Markov chains Gibbs states are given.

We propose a dynamical process for network evolution, aiming at explaining the emergence of the small world phenomenon, i.e., the statistical observation that any pair of individuals are linked by a short chain of acquaintances computable by a simple decentralized routing algorithm, known as greedy routing. Previously proposed dynamical processes enabled to demonstrate experimentally (by simula...

My research interests lie in the areas of dynamical systems and geometry of negatively curved spaces. My thesis is on the dynamics of expanding Thurston maps, and the negatively curved spaces induced by these maps. A dynamical system describes the time dependence of the position of a point in its ambient space under some fixed law. This law describes the evolution of the state of the system ove...

We introduce and study a new optimal transport problem on bounded domain $${{\bar{\Omega }}}\subset {\mathbb {R}}^d$$ , defined via dynamical Benamou–Brenier formulation. The model handles differently the motion in interior boundary, penalizes transfer of mass between two. resulting distance interpolates classical }}}$$ one hand, other hand two independent problems set $$\Omega $$ $${\partial \...

the main goal of the present paper is to extend classical results from the measure theory and dynamical systems to the fuzzy subset setting. in this paper, the notion of  dynamic equivalence relation is introduced and then it is proved that this relation is an equivalence relation. also, a new metric on the collection of all equivalence classes is introduced and it is proved that this metric is...

orography plays a substantial role in the formation and evolution of many atmospheric phenomena. observations indicate that two mountain ranges to the southwest of the red sea and west of iran (zagross mountain range) play a crucial role in the formation, evolution and activities of synoptic weather systems over iran. observations also, indicate that there are considerable differences between t...