Related papers: A common first integral from three-body secular th…
The three-body problem is reexamined in the framework of general relativity. The Newtonian three-body problem admits Euler's collinear solution, where three bodies move around the common center of mass with the same orbital period and…
Consider the dynamics of two point masses on a surface of constant curvature subject to an attractive force analogue of Newton's inverse square law. When the distance between the bodies is sufficiently small, the reduced equations of motion…
We study the secular effects in the motion of an asteroid with negligible mass in a spatial restricted elliptic three body problem with arbitrary inclination. Averaging over mean anomalies of the asteroid and the planet are applied to…
In the recent papers~[18],~[5], respectively, the existence of motions where the perihelions afford periodic oscillations about certain equilibria and the onset of a topological horseshoe have been proved. Such results have been obtained…
We develop a numerical scheme for the Kepler problem that preserves exactly all first integrals: angular momentum, total energy, and the Laplace-Runge-Lenz vector. This property ensures that orbital trajectories retain their precise shape…
We study polygonal billiards with one-sided vertical mirror scattered on a square billiard table. We associate trajectories of these kinds of billiards with double rotations and study orbit behavior and questions of complexity.
We introduce a new method for estimating the growth of various quantities arising in dynamical systems. We apply our method to polygonal billiards on surfaces of constant curvature. For instance, we obtain power bounds of degree two plus…
We use Clifford algebras to construct a unified formalism for studying constant extrinsic curvature immersed surfaces in riemannian and semi-riemannian $3$-manifolds in terms of immersed bilegendrian surfaces in their unitary bundles. As an…
The description of the long-term dynamics of highly elliptic orbits under third-body perturbations may require an expansion of the disturbing function in series of the semi-major axes ratio up to higher orders. To avoid dealing with long…
We consider the Kepler problem on surfaces of revolution that are homeomorphic to $S^2$ and have constant Gaussian curvature. We show that the system is maximally superintegrable, finding constants of motion that generalize the Runge-Lentz…
Recently were introduced physical billiards where a moving particle is a hard sphere rather than a point as in standard mathematical billiards. It has been shown that in the same billiard tables the physical billiards may have totally…
This paper studies bulk-surface splitting methods of first order for (semi-linear) parabolic partial differential equations with dynamic boundary conditions. The proposed Lie splitting scheme is based on a reformulation of the problem as a…
We introduce a circular restricted charged three-body problem on the plane. In this model, the gravitational and Coulomb forces, due to the primary bodies, act on a test particle; the net force exerted by some primary body on the test…
Eigenfunctions of integrable planar billiards are studied - in particular, the number of nodal domains, $\nu$, of the eigenfunctions are considered. The billiards for which the time-independent Schr\"odinger equation (Helmholtz equation) is…
We consider classical dynamical properties of a particle in a constant gravitational force and making specular reflections with circular, elliptic or oval boundaries. The model and collision map are described and a detailed study of the…
We propose a contact-topological approach to the spatial circular restricted three-body problem, for energies below and slightly above the first critical energy value. We prove the existence of a circle family of global hypersurfaces of…
The aim of this work is to continue the analysis, started in arXiv:2105.02108, of the dynamics of a point-mass particle $P$ moving in a galaxy with an harmonic biaxial core, in whose center sits a Keplerian attractive center (e.g. a Black…
The aim of the paper is to unify the efforts in the study of integrable billiards within quadrics in flat and curved spaces and to explore further the interplay of symplectic and contact integrability. As a starting point in this direction,…
We introduce a new class of billiard systems in the plane, with boundaries formed by finitely many arcs of confocal conics such that they contain some reflex angles. Fundamental dynamical, topological, geometric, and arithmetic properties…
We consider a class of random billiards in a tube, where reflection angles at collisions with the boundary of the tube are random variables rather than deterministic (and elastic) quantities. We obtain a (non-standard) Central Limit Theorem…