Related papers: Counting prime orbits in shrinking intervals for e…

In this article, we consider a counting problem for orbits of hyperbolic rational maps on the Riemann sphere, where constraints are placed on the multipliers of orbits. Using arguments from work of Dolgopyat, we consider varying and…

We prove the finiteness of the Zsigmondy set associated to the critical orbit of f(z) = z^d+c for rational values of c by finding an effective bound on the size of the set. For non-recurrent critical orbits, the Zsigmondy set is explicitly…

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…

Analytic methods to investigate periodic orbits in galactic potentials. To evaluate the quality of the approximation of periodic orbits in the logarithmic potential constructed using perturbation theory based on Hamiltonian normal forms.…

Given a point and an expanding map on the unit interval, we consider the set of points for which the forward orbit under this map is bounded away from the given point. For maps like multiplication by an integer modulo 1, such sets have full…

An estimate on the number of distinct relative periodic orbits around a stable relative equilibrium in a Hamiltonian system with continuous symmetry is given. This result constitutes a generalization to the Hamiltonian symmetric framework…

We extend Sharkovskii's theorem to the cases of $N$-dimensional maps which are close to 1D maps, with an attracting $n$-periodic orbit. We prove that, with relatively weak topological assumptions, there exist also $m$-periodic orbits for…

We study higher order expansions both in the Berry-Ess\'een estimate (Edgeworth expansions) and in the local limit theorems for Birkhoff sums of chaotic probability preserving dynamical systems. We establish general results under technical…

Birkhoff normal forms are commonly used in order to ensure the so called "effective stability" in the neighborhood of elliptic equilibrium points for Hamiltonian systems. From a theoretical point of view, this means that the eventual…

Over the last two decades, pseudospectral methods based on Lagrange interpolants have flourished in solving trajectory optimization problems and their flight implementations. In a seemingly unjustified departure from these highly successful…

We study dynamical systems arising as time-dependent compositions of Pomeau-Manneville-type intermittent maps. We establish central limit theorems for appropriately scaled and centered Birkhoff-like partial sums, with estimates on the rate…

We analyze a real one-parameter family of quasiconformal deformations of a hyperbolic rational map known as {\em spinning}. We show that under fairly general hypotheses, the limit of spinning either exists and is unique, or else converges…

We consider rational maps $f$ on the Riemann sphere $\widehat {\mathbb{C}}$ with an $f$-invariant set $P\subset \widehat {\mathbb{C}}$ of four marked points containing the postcritical set of $f$. We show that the dynamics of the…

We consider certain parametrised families of piecewise expanding maps on the interval, and estimate and sometimes calculate the Hausdorff dimension of the set of parameters for which the orbit of a fixed point has a certain shrinking target…

In this manuscript, we consider finitely many maps, all of which are defined on a smooth compact measure space, with at least one map in the collection having degree strictly bigger than 1. Working with random dynamics generated by this…

We show that there is a spectral gap for the transfer operator associated to a rational map f on the Riemann sphere. Using this and the method of pertubed operators we establish the (Local) Central Limit Theorem for the measure of maximal…

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…

Given an exact symplectic map $T$ of a cylinder with a generating function $H$ satisfying the so-called negative twist condition, $H_{12}>0$, we study the locally maximizing orbits of $T$, that is, configurations which are local maxima of…

Thurston maps are branched self-coverings of the sphere whose critical points have finite forward orbits. We give combinatorial and algebraic characterizations of Thurston maps that are isotopic to expanding maps as "Levy-free" maps and as…

In this paper, we give an elementary proof on the existence of an effective uniform upper bound on the size of integral periodic orbits of a single endomorphism in an affine space, dependent solely on its dimension. In fact, we derive a…