Related papers: Hamiltonian Normal Forms and Galactic Potentials
A simple and efficient variational method is introduced to accelerate the convergence of the eigenenergy computations for a Hamiltonian H with singular potentials. Closed-form analytic expressions in N dimensions are obtained for the matrix…
We study two uncoupled oscillators, horizontal and vertical, residing in rectilinear polygons (with only vertical and horizontal sides) and impacting elastically from their boundary. The main purpose of the article is to analyze the…
Contraction analysis establishes exponential incremental convergence of a nonlinear system by solving a linear matrix inequality for a contraction metric, and has become a standard resource for solving problems in nonlinear control and…
In this paper we investigate the gravitational waves emission by stellar dynamical structures as complex systems in the quadrupole approximation considering bounded and unbounded orbits. Precisely, after deriving analytical expressions for…
The information contained in galactic rotation curves is examined under a minimal set of assumptions. If emission occurs from stable circular geodesic orbits of a static spherically symmetric field, with information propagated to us along…
We attempt to get a polynomial solution to the inverse problem, that is, to determine the form of the mechanical Hamiltonian when given the energy spectrum and transition dipole moment matrix. Our approach is to determine the potential in…
This paper is a review of the dynamics of a system of planets. It includes the study of averaged equations in both non-resonant and resonant systems and shows the great deal of situations in which the angle between the two semi-major axes…
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…
The theory of modular forms and spherical harmonic analysis are applied to establish new best bounds towards the counting and equidistribution of rational points on spheres and other higher dimensional ellipsoids, in what may be viewed as a…
We study the essential spectrum, which corresponds to inertia-gravity modes, of the system of equations governing a rotating and self-gravitating gas planet. With certain boundary conditions, we rigorously and precisely characterize the…
In this paper, we give a new construction of resonant normal forms with a small remainder for near-integrable Hamiltonians at a quasi-periodic frequency. The construction is based on the special case of a periodic frequency, a Diophantine…
We present a detailed description of how a differential geometric approach to Hamiltonian dynamics can be used for determining the existence of a crossover between different dynamical regimes in a realistic system, a model of a rare gas…
There are many fundamental aspects of Galactic structure and evolution which can be studied best or exclusively with high quality three dimensional kinematics. Amongst these we note as examples determination of the orientation of the…
We revisit a classical perturbative approach to the Hamiltonian related to the motions of Trojan bodies, in the framework of the Planar Circular Restricted Three-Body Problem (PCRTBP), by introducing a number of key new ideas in the…
We discuss normal forms and symplectic invariants of parabolic orbits and cuspidal tori in integrable Hamiltonian systems with two degrees of freedom. Such singularities appear in many integrable systems in geometry and mathematical physics…
Starting from the study of one-dimensional potentials in quantum mechanics having a small distance behavior described by a harmonic oscillator, we extend this way of analysis to models where such a behavior is not generally expected. In…
Normal form stability estimates are a basic tool of Celestial Mechanics for characterizing the long-term stability of the orbits of natural and artificial bodies. Using high-order normal form constructions, we provide three different…
The paper deals with the problem of existence of a convergent "strong" normal form in the neighbourhood of an equilibrium, for a finite dimensional system of differential equations with analytic and time-dependent non-linear term. The…
The Lyapunov exponents of a chaotic system quantify the exponential divergence of initially nearby trajectories. For Hamiltonian systems the exponents are related to the eigenvalues of a symplectic matrix. We make use of this fact to…
For many applications, critical information about system dynamics is encoded in associated eigenvalue problems that can be posed as linear Hamiltonian systems with suitable boundary conditions. Motivated by examples from hydrodynamics,…