In the context of the dynamical system approach to cognition and supposing that brains or brain-like systems controlling the behavior of autonomous systems are permanently driven by their sensor signals, the paper approaches the question of neurodynamics in the sensorimotor loop in a purely formal way. This is carefully done by addressing the problem in three steps, using the time-discrete dyna...

We begin a systematic study of Euclidean Piecewise Isometric Dynamical Systems (p.i.d.s.) with a particular focus on the interplay between geometry, and symbolic dynamics , and the group of isometries associated with p.i.d.s. We investigate various aspects of the dynamical information contained in the coding: symbolic growth and the periodic behavior of codings and cells. This theoretical inves...

In the paper we investigate the behavior of trajectory of rational p-adic dynamical system in complex p-adic filed Cp. It is studied Siegel disks and attractors of such dynamical systems. We show that Siegel disks may either coincide or disjoin for different fixed points of the dynamical system. Besides, we find the basin of the attractor of the system. It is proved that such kind of dynamical ...

‎In this text we prove that in generalized shift dynamical system $(X^Gamma,sigma_varphi)$‎ ‎for finite discrete $X$ with at least two elements‎, ‎infinite countable set $Gamma$ and‎ ‎arbitrary map $varphi:GammatoGamma$‎, ‎the following statements are equivalent‎: ‎ - the dynamical system $(X^Gamma,sigma_varphi)$ is‎ Li-Yorke chaotic;‎ - the dynamical system $(X^Gamma,sigma_varphi)$ has‎ an scr...