Related papers: Good Reduction of Periodic Points
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…
The periodic points of a morphism of good reduction for a smooth projective curve with good reduction over the p-adics form a discrete set. This is used to give an interpretation of the morphic height in terms of asymptotic properties of…
We prove the effectivity of the dynatomic cycles for morphisms of projective varieties. We then analyze the degrees of the dynatomic cycles and multiplicities of formal periodic points and apply these results to the existence of periodic…
We study the algebraic dynamical systems generated by triangular systems of rational functions and estimate the height growth of iterations generated by such systems. Further, using a result on the reduction modulo primes of systems of…
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…
A case study of arithmetic dynamics over the rationals on the Markoff surface is presented, in particular the local-global dynamical property of strong residual periodicity. The dynamical system induced by the composition of any two of the…
We provide an example of how the complex dynamics of a recently introduced model can be understood via a detailed analysis of its associated Riemann surface. Thanks to this geometric description an explicit formula for the period of the…
Given an endomorphism of a projective variety, by intersecting the graph and the diagonal varieties we can determine the set of periodic points. In an effort to determine the periodic points of a given minimal period, we follow a…
We study a system of intervals $I_1,\ldots,I_k$ on the real line and a continuous map $f$ with $f(I_1 \cup I_2 \cup \ldots \cup I_k)\supseteq I_1 \cup I_2 \cup \ldots \cup I_k$. It's conjectured that there exists a periodic point of period…
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 describe the global dynamics of some pointwise periodic piecewise linear maps in the plane that exhibit interesting dynamic features. For each of these maps we find a first integral. For these integrals the set of values are discrete,…
This article addresses the existence of $\Q$-rational periodic points for morphisms of projective space. In particular, we construct an infinitely family of morphisms on $\P^N$ where each component is a degree 2 homogeneous form in $N+1$…
In this paper we study the monomial dynamical systems of dimension one over finite fields from the viewpoints of arithmetic and graph theory. We give formulas for the number of periodic points with period r and cycles with length r. Then we…
After a preliminary discussion of the relevance of the field nature of gravitation interaction, both for the fundamental interaction of particles and the topology of space time, a method is proposed to produce and detect a dynamical…
Classical relativistic system of point particles coupled with an electromagnetic field is considered in the three-dimensional representation. The gauge freedom connected with the chronometrical invariance of the four-dimensional description…
We give a method to determine relative periodic orbits in point vortex systems: it consists mainly into perform a symplectic reduction on a fixed point submanifold in order to obtain a two-dimensional reduced phase space. The method is…
Several new mutation-periodic quivers of period higher than 1 are introduced as well as the associated discrete dynamical systems. The reduction of these systems is developed using either a presymplectic or a Poisson approach. The…
The dynamics of a linear dynamical system over a finite field can be described by using the elementary divisors of the corresponding matrix. It is natural to extend the investigation to a general finite commutative ring. In a previous…
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…
In this paper we study the time evolution of a class of two-level systems driven by periodic fields in terms of new convergent perturbative expansions for the associated propagator U(t). The main virtue of these expansions is that they do…