Related papers: Periodic Orbits and Escapes in Dynamical Systems
In this work, we study the continuation of a periodic orbit on a relatively large scale and discover the existence of convergence under certain conditions, which has profound significance in research on asteroids and can provide a total…
We consider chaotic (hyperbolic) dynamical systems which have a generating Markov partition. Then, open dynamical systems are built by making one element of a Markov partition a hole through which orbits escape. We compare various estimates…
We investigate the emergence of complex dynamics in a system of coupled dissipative kicked rotors and show that critical transitions can be understood via bifurcations of simple states. We study multistability and bifurcations in the single…
We argue semiclassically, on the basis of Gutzwiller's periodic-orbit theory, that full classical chaos is paralleled by quantum energy spectra with universal spectral statistics, in agreement with random-matrix theory. For dynamics from…
We present an adaptation of a relatively simple topological argument to show the existence of many periodic orbits in an infinite dimensional dynamical system, provided that the system is close to a one-dimensional map in a certain sense.…
A well-behaved adjoint sensitivity technique for chaotic dynamical systems is presented. The method arises from the specialisation of established variational techniques to the unstable periodic orbits of the system. On such trajectories,…
A classical double oscillator model, that includes in certain parameter limits, the standard harmonic oscillator and the inverse oscillator, is interpreted as a dynamical system. We study its essential features and make a qualitative…
We derive an analytical trace formula for the level density of the two-dimensional elliptic billiard using an improved stationary phase method. The result is a continuous function of the deformation parameter (eccentricity) through all…
We numerically investigate the orbital dynamics of a two-dimensional galactic model, emphasizing the influence of stable and unstable manifolds on the evolution of orbits. In our analysis we use evaluations of the system's Lagrangian…
Periodic orbits are fundamental to understand the dynamics of nonlinear systems. In this work, we focus on two aspects of interest regarding periodic orbits, in the context of a dissipative mapping, derived from a prototype model of a…
The motion of a satellite around a planet can be studied by the Hill model, which is a modification of the restricted three body problem pertaining to motion of a satellite around a planet. Although the dynamics of the circular Hill model…
We consider a dynamical system given by an area-preserving map on a two-dimensional phase plane and consider a one-dimensional line of initial conditions within this plane. We record the number of iterates it takes a trajectory to escape…
The existence of stable periodic orbits and chaotic invariant sets of singularly perturbed problems of fast-slow type having Bogdanov-Takens bifurcation points in its fast subsystem is proved by means of the geometric singular perturbation…
This paper investigates the difference between the circular and elliptical cases in one-on-one pursuit and evasion problems. Using the simultaneous differential equation derived by Barton and Eliezer, we derive a dynamical system based on…
In this paper, we study the existence of bifurcation of a van der Pol-Duffing oscillator with quintic terms and its quasi-periodic solutions by means of qualitative and bifurcation theories. Firstly, we analyze the autonomous system and…
We investigate the multiple bifurcations in periodic orbit families in the potential field of a highly irregular-shaped celestial body. Topological cases of periodic orbits and four kinds of basic bifurcations in periodic orbit families are…
A system plus environment conservative model is used to characterize the nonlinear dynamics when the time averaged energy for the system particle starts to decay. The system particle dynamics is regular for low values of the $N$ environment…
Systems of coaxial vortex pairs in an inviscid flow give rise to complex dynamics, with motions ranging from ordered to chaotic. This complexity arises due to the problem's high nonlinearity and numerous degrees of freedom. We analyze the…
We study the dynamics in the neighborhood of simple and double unstable periodic orbits in a rotating 3D autonomous Hamiltonian system of galactic type. In order to visualize the four dimensional spaces of section we use the method of color…
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…