Related papers: Hamiltonian Normal Forms and Galactic Potentials
Extending previous work with Lattanzio and Mascia on the scalar (in fluid-dynamical variables) Hamer model for a radiative gas, we show nonlinear orbital asymptotic stability of small-amplitude shock profiles of general systems of coupled…
The technique of "extension" allows to build $(n+1)$-dimensional Hamiltonian systems with a non-trivial polynomial in the momenta first integral of any given degree starting from a $n$-dimensional Hamiltonian satisfying some additional…
As countless examples show, it can be fruitful to study a sequence of complicated objects all at once via the formalism of generating functions. We apply this point of view to the homology and combinatorics of orbit configuration spaces:…
Recent works demonstrated that the dynamics caused by the planetary oblateness coupled with the solar radiation pressure can be described through a model based on singly-averaged equations of motion. The coupled perturbations affect the…
A special form of the isotropic metric in cylindrical coordinates is used to construct what may be interpreted as the General Relativistic versions of some wellknown potential-density pairs used in Newtonian gravity to model…
We introduce a one-dimensional toy model of globular clusters. The model is a version of the well-known gravitational sheets system, where we take additionally into account mass and energy loss by evaporation of stars at the boundaries.…
We use Moser's normal forms to study chaotic motion in two-degree hamiltonian systems near a saddle point. Besides being convergent, they provide a suitable description of the cylindrical topology of the chaotic flow in that vicinity. Both…
We consider a classical system of n charged particles in an external confining potential, in any dimension d larger than 2. The particles interact via pairwise repulsive Coulomb forces and the coupling parameter scales like the inverse of n…
Statistical physics models ranging from simple lattice to complex quantum Hamiltonians are one of the mainstays of modern physics, that have allowed both decades of scientific discovery and provided a universal framework to understand a…
We consider families of Hamiltonian systems in two degrees of freedom with an equilibrium in 1:2 resonance. Under detuning, this "Fermi resonance" typically leads to normal modes losing their stability through period-doubling bifurcations.…
One of the major goals of the field of Milky Way dynamics is to recover the gravitational potential field. Mapping the potential would allow us to determine the spatial distribution of matter - both baryonic and dark - throughout the…
The simple, longitudinal, and transverse wobblers are systematically studied within the framework of collective Hamiltonian, where the collective potential and mass parameter included are obtained based on the tilted axis cranking approach.…
The potential concept that is successful in classical electrodynamics should also be applicable to the nonlinear electromagnetic forces acting on matter. The obvious method of determining these potentials should be provided by Helmholtz's…
We use physical constrains imposed from the H-Theorem and from the negative nature of the heat capacity of self-gravitating thermodynamically isolated systems to investigate some possible limits on the stellar polytrope index $n$ within the…
We study the dynamics of a damped harmonic oscillator in the presence of a retarded potential with state-dependent time-delayed feedback. In the limit of small time-delays, we show that the oscillator is equivalent to a Li\'enard system.…
We first discuss the use of dimensional arguments (and of the quadrupolar emission hypothesis) in the derivation of the gravitational power radiated on a circular orbit. Then, we show how to simply obtain the instantaneous power radiated on…
Accurately learning the temporal behavior of dynamical systems requires models with well-chosen learning biases. Recent innovations embed the Hamiltonian and Lagrangian formalisms into neural networks and demonstrate a significant…
A framework for identifying nonlinear port-Hamiltonian systems using input-state-output data is introduced. The framework utilizes neural networks' universal approximation capacity to effectively represent complex dynamics in a structured…
Many experimental techniques aim at determining the Hamiltonian of a given system. The Hamiltonian describes the system's evolution in the absence of dissipation, and is often central to control or interpret an experiment. Here, we…
We present a large deviation analysis of a recently proposed probabilistic approach to the study of the ground-state properties of lattice quantum systems. The ground-state energy, as well as the correlation functions in the ground state,…