Related papers: Alternative method to find orbits in chaotic syste…
We present a computational scheme based on classical molecular dynamics to study chaotic billiards in static external magnetic fields. The method allows to treat arbitrary geometries and several interacting particles. We test the scheme for…
This paper examines the use of operator-theoretic approaches to the analysis of chaotic systems through the lens of their unstable periodic orbits (UPOs). Our approach involves three data-driven steps for detecting, identifying, and…
Astrophysical objects frequently exhibit some irregularities or complex behaviour in their light curves. We focus primarily on hot stars, where both radial and non-radial pulsations are observed. One of the primary research goals is to…
Recent progress of symbolic dynamics of one- and especially two-dimensional maps has enabled us to construct symbolic dynamics for systems of ordinary differential equations (ODEs). Numerical study under the guidance of symbolic dynamics is…
A systematic numerical technique for the calculation of unstable periodic orbits in the stadium billiard is presented. All the periodic orbits up to order $p=11$ are calculated and then used to calculate the average Lyapunov exponent and…
The dynamics of chaotic billiards is significantly influenced by coexisting regions of regular motion. Here we investigate the prevalence of a different fundamental structure, which is formed by marginally unstable periodic orbits and…
We report on the application of chaos control to the irregular motion of an electron under the combined influence of a Coulomb and a magnetic field, the so-called ``diamagnetic Kepler problem'' (DKP). We show how to stabilize the classical…
In the current study, the existence of periodic orbits around a fixed homogeneous cube is investigated, and the results have powerful implications for examining periodic orbits around non-spherical celestial bodies. In the two different…
Chaotic dynamics can be quite heterogeneous in the sense that in some regions the dynamics are unstable in more directions than in other regions. When trajectories wander between these regions, the dynamics is complicated. We say a chaotic…
Classical chaotic systems with symbolic dynamics but strong pruning present a particular challenge for the application of semiclassical quantization methods. In the present study we show that the technique of periodic orbit quantization by…
We examine a strange chaotic attractor and its unstable periodic orbits in case of one degree of freedom nonlinear oscillator with non symmetric potential. We propose an efficient method of chaos control stabilizing these orbits by a…
The theory of the inverse problem is used in order to find a two dimensional galactic potential generating a mono-parametric family of elliptic periodic orbits. The potential is made up of a two-dimensional harmonic oscillator with…
In this paper we develop further a method for detecting unstable periodic orbits (UPOs) by stabilising transformations, where the strategy is to transform the system of interest in such a way that the orbits become stable. The main…
We consider the motion of a particle subjected to the constant gravitational field and scattered inelasticaly by hard boundaries which possess the shape of parabola, wedge, and hyperbola. The billiard itself performs oscillations. The…
A variational principle for determining unstable periodic orbits of flows as well as unstable spatio-temporally periodic solutions of extended systems is proposed and implemented. An initial loop approximating a periodic solution is evolved…
In the helium case of the classical Coulomb three-body problem in two dimensions with zero angular momentum, we develop a procedure to find periodic orbits applying two symbolic dynamics for one-dimensional and planar problems. A sequence…
We introduce a class of billiards with chaotic unidirectional flows (or non-chaotic unidirectional flows with "vortices") which go around a chaotic or non-chaotic "core", where orbits can change their orientation. Moreover, the…
This paper discusses applications of a particular control technique that can be used to very efficiently stabilize a chaotic system onto a large subset of the unstable periodic orbits that are typically embedded in the system. The control…
In Hamiltonian systems subjected to periodic perturbations the stable and unstable manifolds of the unstable periodic orbits provide the dynamical "skeleton" that drives the mixing process and bounds the chaotic regions of the phase space.…
By folding an autonomous system of rational equations in the plane to a scalar difference equation, we show that the rational system has coexisting periodic orbits of all possible periods as well as stable aperiodic orbits for certain…