Related papers: Discretized rotation has infinitely many periodic …
We introduce a new definition of distinguished trajectory that generalises the concepts of fixed point and periodic orbit to aperiodic dynamical systems. This new definition is valid for identifying distinguished trajectories with…
This paper deals with the dynamics of discretizations of isometries of $\mathbf R^n$, and more precisely the density of the successive images of $\mathbf Z^n$ by the discretizations of a generic sequence of isometries. We show that this…
We study discrete-time random dynamical systems where each fibre map is an orientation-preserving homeomorphism of the circle. We prove that the existence of a random periodic cycle with period at least two implies that the random rotation…
We investigate the qualitative characteristics of a test particle attracted to an irregular elongated body, modeled as a non-homogeneous straight segment with a variable linear density. By deriving the potential function in closed form, we…
We consider the space of all representations of the commutator subgroup of a knot group into Z/p, p is prime. As proven by D. Silver and S. Williams, this space can be completely described by a finite oriented graph. We describe the lengths…
We prove that two finite endomorphisms of the unit disk with degree at least two have orbits with infinite intersections if and only if they have a common iteration.
We study the dynamics of multidimensional contracted rotations and address a problem posed by Y. Bugeaud and J-P. Conze in \textit{Acta Arithmetica} in 1999. More precisely, we show that if $A$ is an invertible linear contraction of…
We investigate the trajectory of an arbitrary $(2,1)$-rational $p$-adic dynamical system in a complex $p$-adic field $\C_p$. (i) In the case where there is no fixed point we show that the $p$-adic dynamical system has a 2-periodic cycle…
The orbits of the reversible differential system $\dot{x}=-y$, $\dot{y}=x$, $\dot{z}=0$, with $x,y \in R$ and $z\in R^d$, are periodic with the exception of the equilibrium points $(0,0, z)$. We compute the maximum number of limit cycles…
We establish a deterministic technique to investigate transport moments of arbitrary order. The theory is applied to the analysis of different kinds of intermittent one-dimensional maps and the Lorentz gas with infinite horizon: the typical…
We consider the periodic model introduced in [20] and disprove the conjectures on the number of periodic orbits the model can have. We rebuild the conjecture to prove that for periodic sequences of maps of any period, the number of non-zero…
We show that polynomial recursions $x_{n+1}=x_{n}^{m}-k$ where $k,m$ are integers and $m$ is positive have no nontrivial periodic integral orbits for $m\geq3$. If $m=2$ then the recursion has integral two-cycles for infinitely many values…
The main theme of this paper is the connection between the existence of infinitely many periodic orbits for a Hamiltonian system and the behavior of its action or index spectrum under iterations. We use the action and index spectra to show…
From our sample of spotted late-type stars showing surface differential rotation we find that the relationship between the rotation period and the surface shear coefficient $\alpha=\Delta\Omega/\Omega_{\rm eq}$ is significantly different…
The Stark problem is Kepler problem with an external constant acceleration. In this paper, we study the periodic orbits for Stark problem for both planar case and spatial case. We have conducted a detailed analysis of the invariant tori and…
We give an algebraic characterization of when a $d$-dimensional periodic framework has no non-trivial, symmetry preserving, motion for any choice of periodicity lattice. Our condition is decidable, and we provide a simple algorithm that…
Reducing motion of particles to a two-dimensional potential problem, we show that there are stable circular orbits around a squashed Kaluza-Klein black hole with a spherical horizon and multi-Kaluza-Klein black holes with two spherical…
We show that for any natural number n, the set of domains containing absolutely periodic orbits of order n are dense in the set of bounded strictly convex domains with smooth boundary. The proof that such an orbit exists is an extension to…
Orbits in different dispersive billiard systems, e.g. the 3 disk system, are mapped into a topological well ordered symbol plane and it is showed that forbidden and allowed orbits are separated by a monotone pruning front. The pruning front…
Time delayed feedback control is one of the most successful methods to discover dynamically unstable features of a dynamical system in an experiment. This approach feeds back only terms that depend on the difference between the current…