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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…
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…
For a fixed k in (-2,2), the discretized rotation on Z^2 is defined by (x,y)->(y,-[x+ky]). We prove that this dynamics has infinitely many periodic orbits.
Periodic solutions of the three body problem are very important for understanding its dynamics either in a theoretical framework or in various applications in celestial mechanics. In this paper we discuss the computation and continuation of…
In a topological dynamical system the complexity of an orbit is a measure of the amount of information (algorithmic information content) that is necessary to describe the orbit. This indicator is invariant up to topological conjugation. We…
Periodic orbit theory allows calculations of long time properties of chaotic systems from traces, dynamical zeta functions and spectral determinants of deterministic evolution operators, which are in turn evaluated in terms of periodic…
The correct computation of orbits of discrete dynamical systems on the interval is considered. Therefore, an arbitrary-precision floating-point approach based on automatic error analysis is chosen and a general algorithm is presented. The…
The finest state space resolution that can be achieved in a physical dynamical system is limited by the presence of noise. In the weak-noise approximation the neighborhoods of deterministic periodic orbits can be computed as distributions…
Linear finite dynamical systems play an important role, for example, in coding theory and simulations. Methods for analyzing such systems are often restricted to cases in which the system is defined over a field %and usually strive to…
We study the relationship between pairs of topological dynamical systems $ (X,T) $ and $ (X',T') $, where $ (X',T') $ is the quotient of $ (X,T) $ under the action of a finite group $ G $. We describe three phenomena concerning the…
In this paper, we will study the statistical behaviors of orbits. Firstly, we will show that for a dynamical systems have the shadowing property or almost specification property, the set of nonrecurrent points has full topological entropy.…
For X a finite subset of the circle and for 0 < r <= 1 fixed, consider the function f_r : X -> X which maps each point to the clockwise furthest element of X within angular distance less than 2 pi r. We study the discrete dynamical system…
We describe the orbit structure for the action of the centralizer group of a linear operator on a finite-dimensional complex vector space. The main application is to the classification of solutions to a system of first-order ODEs with…
Periodic orbits are important objects of discrete dynamical systems, but finding them is not always easy. We present a self-contained introductory account, aimed at non-experts, to prove their existence and study their stability using the…
By varying a parameter of a one-dimensional piecewise smooth map, stable periodic orbits are observed. In this paper, complete analytic characterization of these stable periodic orbits is obtained. An interesting relationship between the…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
Motivated by work of Kucharczyk and Scholze, we use sheafified rational Witt vectors to attach a new ringed space $W_{\mathrm{rat}} (X)$ to every scheme $X$. We also define $R$-valued points $W_{\mathrm{rat}} (X) (R)$ of $W_{\mathrm{rat}}…
Establishing the existence of periodic orbits is one of the crucial and most intricate topics in the study of dynamical systems, and over the years, many methods have been developed to this end. On the other hand, finding closed orbits in…
We provide a constructive method designed in order to control the stability of a given periodic orbit of a general completely integrable system. The method consists of a specific type of perturbation, such that the resulting perturbed…
In this work, applying general results from averaging theory, we find periodic orbits for a class of Hamiltonian systems $H$ whose potential models the motion of elliptic galaxies.