Related papers: Instabilities and chaos in the classical three-bod…
We use perturbation theory and bifurcation theory to analyze the dynamical behavior of resonances, associated to a model describing a particle moving within a ring around a celestial object. The central body is modeled as a homogeneous…
Linear equations with periodic coefficients describe the behavior of various dynamical systems. This studying is devoted to their applications to the planetary restricted three-body problem (RTBP). Here we consider the Laplace method for…
Using the properties of the angular momentum, we develop a new geometrical technique to study relative equilibria for a system of $3$--bodies with positive masses, moving on the two sphere under the influence of an attractive potential…
When the planar circular restricted 3-body problem (RTBP) is periodically perturbed, families of unstable periodic orbits break up into whiskered tori, with most tori persisting into the perturbed system. In this study, we 1) develop a…
In this work we revisit the geometric approach to chaos in Hamiltonian dynamics, by means of the Jacobi-Levi-Civita equation (JLCE). We inspect numerically two low-dimensional dynamical systems; show that, along chaotic orbits, the…
Context. The study of linear waves and instabilities is necessary to understand the physical evolution of an atmosphere, and can provide physical interpretation of the complex flows found in simulations performed using Global Circulation…
Chaotic motion in time of a number of macroscopic systems has been analyzed, in the framework of scale relativity, as motion in a fractal space with topological dimension 3 and geodesics with fractal dimension 2. The motion equation is then…
FRW cosmologies with conformally coupled scalar fields are investigated in a geometrical way by the means of geodesics of the Jacobi metric. In this model of dynamics, trajectories in the configuration space are represented by geodesics.…
In geometric algebra, the rotation of a vector is described using rotors. Rotors are phasors where the imaginary number has been replaced by a oriented plane element of unit area called a unit bivector. The algebra in three dimensional…
In this paper, we consider the elliptic collinear solutions of the classical $n$-body problem, where the $n$ bodies always stay on a straight line, and each of them moves on its own elliptic orbit with the same eccentricity. Such a motion…
We show that Gutzwiller's characterization of chaotic Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor in the structure of the Hamiltonian can be extended to a wide class of potential models of…
We studied complex spectra of spin-two boson systems represented by E$\otimes$e and E$\otimes (b_1+b_2)$ Jahn-Teller models. For E$\otimes$e, at particular rotation quantum numbers we found a coexistence of up to three regions of the…
This paper investigates the restricted circular planar three-body problem. We prove that for every negative Jacobi constant of sufficiently large magnitude, the surface of unperturbed parabolic solutions breaks to induce homoclinic tangle…
In this paper, we study the linear stability of the elliptic rhombus solutions, which are the Keplerian homographic solution with the rhombus central configurations in the classical planar four-body problems. Using $\omega$-Maslov index…
In this letter we show that although the application of standard Lyapunov analysis predicts that completely integrable Kepler motion is unstable, the geometrical analysis of Horwitz et al [1] predicts the observed stability. This seems to…
Let a number, N, of particles interact classically through Newton's Laws of Motion and Newton's inverse square Law of Gravitation. The resulting equations of motion provide an approximate mathematical model with numerous applications in…
In this paper, we consider the linear stability of the elliptic relative equilibria of the restricted 4-body problems where the three primaries form a Lagrangian triangle. By reduction, the linearized Poincar\'e map is decomposed to the…
Developing measures of quantum ergodicity and chaos stands as a foundational task in the study of quantum many-body systems. In this work, we propose metrics for these effects based on Hamiltonian learning that unify multiple advantages of…
The classical and quantum dynamics of two ultra-strongly coupled and weakly nonlinear resonators cannot be explained using the Discrete Nonlinear Schr\"odinger Equation or the Bose-Hubbard model, respectively. Instead, a model beyond the…
In a fully 3-D system such as a stellarator, the toroidal mode number $n$ ceases to be a good quantum number--all $n$s within a given mode family being coupled. It is found that the discrete spectrum of unstable ideal MHD…