相关论文: Analysis of Stable Periodic Orbits in 1-D Linear P…

We study the dynamics of piecewise conformal maps in the Riemann sphere. The normality and chaotic regions are defined and we state several results and properties of these sets. We show that the stability of these piecewise maps is related…

We consider delay differential equations of the form $ y'(t)=-ay(t)+bf(y(t-1)) $ with positive parameters $a,b$ and a unimodal $f:[0,\infty)\to [0,1]$. It is assumed that the nonlinear $f$ is close to a function $g:[0,\infty)\to [0,1]$ with…

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 prove the existence of $n$-periodic orbits for almost all $n\in\mathbb{N}$ in the R\"ossler system with attracting periodic orbit, for two sets of parameters. The proofs are computer-assisted.

We consider a cubic nonlinear wave equation on a network and show that inspecting the normal modes of the graph, we can immediately identify which ones extend into nonlinear periodic orbits. Two main classes of nonlinear periodic orbits…

We consider functional differential equations(FDEs) which are perturbations of smooth ordinary differential equations(ODEs). The FDE can involve multiple state-dependent delays or distributed delays (forward or backward). We show that,…

In this paper we establish the orbital stability of periodic waves related to the logarithmic Korteweg-de Vries equation. Our motivation is inspired in the recent work \cite{carles}, in which the authors established the well-posedness and…

We consider piecewise expanding maps of the interval with finitely many branches of monotonicity and show that they are generically combinatorially stable, i.e., the number of ergodic attractors and their corresponding mixing periods do not…

The phenomenology of a system of two coupled quadratic maps is studied both analytically and numerically. Conditions for synchronization are given and the bifurcations of periodic orbits from this regime are identified. In addition, we show…

In this paper, we identify criteria that guarantees the nonlinear orbital stability of a given periodic traveling wave solution within the b-family Camassa-Holm equation. These periodic waves exist as 3-parameter families (up to spatial…

The quest of exo-Earths has become a prominent field. In this work, we study the stability of non-coplanar planetary configurations consisting of an inclined inner terrestrial planet in mean-motion resonance with an outer giant planet. We…

An algorithm for detecting periodic orbits in chaotic systems [Phys. Rev. E, 60 (1999), pp.~6172--6175], which combines the set of stabilising transformations proposed by Schmelcher and Diakonos [Phys. Rev. Lett., 78 (1997), pp.~4733--4736]…

The existence of smooth periodic traveling solutions in the Dullin-Gottwald-Holm (DGH) equation and the monotonicity of the period function are clarified. By introducing two suitable parameters, we show the existence of periodic travelling…

Periodic orbits (equivalence classes of closed paths up to cyclic shifts) play an important role in applications of graph theory. For example, they appear in the definition of the Ihara zeta function and exact trace formulae for the spectra…

In this article, we study the behaviour of discrete one-dimensional dynamical systems associated to functions on finite sets. We formalise the global orbit pattern formed by all the periodic orbits (gop) as the ordered set of periods when…

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…

In the paper below we consider a problem of stabilization of a priori unknown unstable periodic orbits in non-linear autonomous discrete dynamical systems. We suggest a generalization of a non-linear DFC scheme to improve the rate of…

The aim of this paper is to numerically investigate the orbital dynamics of the circular planar restricted problem of five bodies. By numerically integrating several large sets of initial conditions of orbits we classify them into three…

The study of circular orbits in spacetime is of astrophysical importance. The identification and classification of circular orbits in both static and stationary spacetimes remains an active area of interest. Even in the simplest static…

We prove the existence of an effective universal upper bound for the order of any integral periodic orbit of any integral algebraic dynamical system in a fixed ambient space. Using this, we demonstrate the decidability of periodicity in…