Related papers: On a non-linear $p$-adic dynamical system
This paper is an extension of an earlier paper that dealt with global dynamics in autonomous triangular maps. In the current paper, we extend the results on global dynamics of autonomous triangular maps to periodic non-autonomous triangular…
Resonantly forced spiral waves in excitable media drift in straight-line paths, their rotation centers behaving as point-like objects moving along trajectories with a constant velocity. Interaction with medium boundaries alters this…
We prove dynamical local limits for the singular numbers of $p$-adic random matrix products at both the bulk and edge. The limit object which we construct, the reflecting Poisson sea, may thus be viewed as a $p$-adic analogue of line…
We investigate the convergence towards periodic orbits in discrete dynamical systems. We examine the probability that a randomly chosen point converges to a particular neighborhood of a periodic orbit in a fixed number of iterations, and we…
We consider an incompressible fluid contained in a toroidal stratum which is only subjected to Newtonian self-attraction. Under the assumption of infinitesimal tickness of the stratum we show the existence of stationary motions during which…
Let $f:\mathcal{M}\rightarrow\mathcal{M}$ be a continuous map defined on a compact metric space $\mathcal{M}$. An open dynamical system introduces disjoint open balls centered at points in $\mathcal{M}$, and considers the trajectories of…
Monomial mappings, $x\mapsto x^n$, are topologically transitive and ergodic with respect to Haar measure on the unit circle in the complex plane. In this paper we obtain an anologous result for monomial dynamical systems over $p-$adic…
In this paper, we study the steady solutions of Euler-Poisson equations in bounded domains with prescribed angular velocity. This models a rotating Newtonian star consisting of a compressible perfect fluid with given equation of state…
Let $K$ be a global function field of characteristic $p$ and degree $D$ over $\mathbb F_{p}(t)$. We consider dynamical systems over the projective line $\mathbb P^1(K)$ defined by rational maps with at most one prime of bad reduction. The…
Intermittent dynamics is characterized by long periods of different types of dynamical characteristics, for instance almost periodic dynamics alternated by chaotic dynamics. Critical intermittency is intermittent dynamics that can occur in…
The main purpose of this article is to study box dimension of orbits near hyperbolic and nonhyperbolic fixed points of discrete dynamical systems in higher dimensions. We generalize the known results for one-dimensional systems, that is,…
Mathematical billiards is much like the real game: a point mass, representing the ball, rolls in a straight line on a (perfectly friction-less) table, striking the sides according to the law of reflection. A billiard trajectory is then…
We show that for periodic non-autonomous discrete dynamical systems, even when a common fixed point for each of the autonomous associated dynamical systems is repeller, this fixed point can became a local attractor for the whole system,…
In a planetary or satellite system, idealized as n small bodies in initially coplanar, concentric orbits around a large central body, obeying Newtonian point-particle mechanics, resonant perturbations will cause dynamical evolution of the…
This review is devoted to dynamical systems in fields of $p$-adic numbers: origin of $p$-adic dynamics in $p$-adic theoretical physics (string theory, quantum mechanics and field theory, spin glasses), continuous dynamical systems and…
We study the dynamics of circular active particles (AP) on a two dimensional periodic undulated surface. Each particle has an internal energy mechanism which is modeled by an active friction force and it is controlled by an activity…
We introduce a two-dimensional discrete-time dynamical system which represents the evolution of an angle and angular velocity. While the angle evolves by a fixed amount in every step, the evolution of the angular velocity is governed by a…
We investigate the dynamical motion of particles on a two-dimensional symmetric periodic substrate in the presence of both a dc drive along a symmetry direction of the periodic substrate and an additional circular ac drive. For large enough…
A broad range of nonlinear processes over networks are governed by threshold dynamics. So far, existing mathematical theory characterizing the behavior of such systems has largely been concerned with the case where the thresholds are…
We study a three dimensional continuous model of gravitating matter rotating at constant angular velocity. In the rotating reference frame, by a finite dimensional reduction, we prove the existence of non radial stationary solutions whose…