Related papers: Chaotic dynamics in the (47171) Lempo triple syste…
We introduce a new analytical method, which allows to find out chaotic dynamics in non-smooth dynamical systems. A simple mechanical system consisting of a mass and a dry friction element is considered as an example. The corresponding…
Several studies have already considered the influence of tides on the evolution of systems composed of a star and a close-in companion to tentatively explain different observations such as the spin-up of some stars with hot Jupiters, the…
Recent numerical results seem to suggest that in certain regimes of typical particle velocities the gravitational $N-$body problem (for $3\leq N\lesssim 10^3$) is intrinsically less chaotic when the post-Newtonian (PN) force terms are…
We consider the 3-body problem in relativistic lineal gravity and obtain an exact expression for its Hamiltonian and equations of motion. While general-relativistic effects yield more tightly-bound orbits of higher frequency compared to…
We used the N-body code of Hernquist and Ostriker (1992) to build a dozen cuspy ({\gamma}\approx 1) triaxial models of stellar systems through dissipationless collapses of initially spherical distributions of 10^6 particles. We chose four…
Orbits in the principal planes of triaxial potentials are known to be prone to unstable motion normal to those planes, so that three dimensional investigations of those orbits are needed even though they are two dimensional. We present here…
The R\"ossler System is one of the best known chaotic dynamical systems, exhibiting a plethora of complex phenomena - and yet, only a few studies tackled its complexity analytically. In this paper we find sufficient conditions for the…
We study the orbital structure of a self-consistent N-body equilibrium configuration of a barred galaxy constructed from cosmological initial conditions. The value of its spin parameter L is near the observed value of our Galaxy L=0.22. We…
We revisit the global modes and instabilities of homogeneous rotating ellipsoidal fluid masses, which are the simplest global models of rotationally and tidally deformed gaseous planets or stars. The tidal flow in a short-period planet may…
In this paper we present a new bootstrap procedure for elliptic systems with two unknown functions. Combining with the $L^p$-$L^q$-estimates, it yields the optimal $L^\infty$-regularity conditions for the three well-known types of weak…
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…
The dynamical properties of a particle in a gravitational field colliding with a rigid wall moving with piecewise constant velocity are studied. The linear nature of the wall's motion permits further analytical investigation than is…
The classical dynamics of two electrons in the Coulomb potential of an attractive nucleus is chaotic in large parts of the high-dimensional phase space. Quantum spectra of two-electron atoms, however, exhibit structures which clearly hint…
A very few three-dimensional (3D) periodic orbits of general three-body problem (with three finite masses) have been discovered since Newton mentioned it in 1680s. Using a high-accuracy numerical strategy we discovered 10,059…
Recent progress toward classifying low-dimensional chaos measured from time series data is described. This classification theory assigns a template to the time series once the time series is embedded in three dimensions. The template…
We analyze the quantum dynamics of periodically driven, disordered systems in the presence of long-range interactions. Focusing on the stability of discrete time crystalline (DTC) order in such systems, we use a perturbative procedure to…
Dynamical equations are formulated and a numerical study is provided for self-oscillatory model systems based on the triple linkage hinge mechanism of Thurston -- Weeks -- Hunt -- MacKay. We consider systems with holonomic mechanical…
We describe the structure of bifurcations in the unbounded classical Diamagnetic Kepler problem. We conjecture that this system does not have any stable orbits and that the non-wandering set is described by a complete trinary symbolic…
We demonstrate the remarkable effectiveness of boundary value formulations coupled to numerical continuation for the computation of stable and unstable manifolds in systems of ordinary differential equations. Specifically, we consider the…
We study the dynamics and the phase-space structures of Coulombic and self-gravitating versions of the classical one-dimensional 3-body system with periodic boundary conditions. We demonstrate that such a 3-body system may be reduced…