Related papers: Chaotic quasi-collision trajectories in the 3-cent…
Accessing the connection between classical chaos and quantum many-body systems has been a long-standing experimental challenge. Here, we investigate the onset of chaos in periodically driven two-component Bose-Einstein condensates, whose…
Motivated by Furstenberg's Theorem on sets in the circle invariant under multiplication by a non-lacunary semigroup, we define a general class of dynamical systems possessing similar topological dynamical properties. We call such systems…
In this work, we investigate the Earth-Moon system, as modeled by the planar circular restricted three-body problem, and relate its dynamical properties to the underlying structure associated with specific invariant manifolds. We consider a…
By introducing a new coordinate system, we prove that there are abundant new periodic orbits near relative equilibrium solutions of the N-body problem. We consider only Lagrange relative equilibrium of the three-body problem and…
In this paper, we consider some cubic near-Hamiltonian systems obtained from perturbing the symmetric cubic Hamiltonian system with two symmetric singular points by cubic polynomials. First, following Han [2012] we develop a method to study…
This paper investigates the secular motion of a massless asteroid within the framework of the double-averaged elliptic restricted three-body problem. By employing Poincar\'e variables, we analyze the stability properties of asteroid orbits…
We investigate the (conservative) dynamics of binary black holes using the Hamiltonian formulation of the post-Newtonian (PN) equations of motion. The Hamiltonian we use includes spin-orbit coupling, spin-spin coupling, and mass…
In this paper we review a recently developed approximate method for investigation of dynamics of compressible ellipsoidal figures. Collapse and subsequent behaviour are described by a system of ordinary differential equations for time…
We show that the probability distribution function that best fits the distribution of return times between two consecutive visits of a chaotic trajectory to finite size regions in phase space deviates from the exponential statistics by a…
We summarize various cases where chaotic orbits can be described analytically. First we consider the case of a magnetic bottle where we have non-resonant and resonant ordered and chaotic orbits. In the sequence we consider the hyperbolic…
We give a qualitative description of two main routes to chaos in three-dimensional maps. We discuss Shilnikov scenario of transition to spiral chaos and a scenario of transition to discrete Lorenz-like and figure-eight strange attractors.…
The character of motion (regular or chaotic) on the quantum level manifests itself in the statistics of the set of the system's energy levels. The completely regular case generates the sequence of the levels with exponential (Poisson) level…
The Restricted 3-Body Problem models the motion of a body of negligible mass under the gravitational influence of two massive bodies, called the primaries. If the primaries perform circular motions and the massless body is coplanar with…
Theoretical foundations of chaos have have been predominantly laid out for finite-dimensional dynamical systems, such as the three-body problem in classical mechanics and the Lorenz model in dissipative systems. In contrast, many real-world…
Goal of the presented research is to construct simplified model of the core-halo structures in binary systems. Examples are provided by Thorne-Zytkov objects, hot Jupiters, protoplanets with large moons, red supergiants in binaries and…
We find a novel characteristic for chaotic motion by introducing Shannon entropy for periodic orbits, quasiperiodic orbits, and chaotic orbits.We compare our approach with the previous methods including Poincar\'{e} Section, Lyapunov…
We study the motion of a charged particle in a tokamak magnetic field and discuss its chaotic nature. Contrary to most of recent studies, we do not make any assumption on any constant of the motion and solve numerically the cyclotron…
The planetary dynamics of $4/3$, $3/2$, $5/2$, $3/1$ and $4/1$ mean motion resonances is studied by using the model of the general three body problem in a rotating frame and by determining families of periodic orbits for each resonance.…
Chaos as typical property of non-linear systems has revealed its crucial role in various problems of astrophysics and cosmology. The problems discussed at these lectures include planetary dynamics, galactic dynamics, reconstruction of the…
We study the dynamics of a three-mode bosonic system with mode-changing interactions. For large mode occupations the short-time dynamics is well described by classical mean-field equations allowing us to study chaotic dynamics in the…