Related papers: Generalized Normal Forms of Two-Dimensional Autono…
We develop a theory of integrable dispersive deformations of 2+1 dimensional Hamiltonian systems of hydrodynamic type following the scheme proposed by Dubrovin and his collaborators in 1+1 dimensions. Our results show that the…
Let $\mathbb{N}^{d}$ be the $d$-dimensional monoid of non-negative integers. A generalized numerical semigroup is a submonoid $ S\subseteq \mathbb{N}^d$ such that $H(S)=\mathbb{N}^d \setminus S$ is a finite set. We introduce irreducible…
Many important physical systems can be described as the evolution of a Hamiltonian system, which has the important property of being conservative, that is, energy is conserved throughout the evolution. Physics Informed Neural Networks and…
We show that the single-mode parafermionic type systems possess supersymmetry, which is based on the symmetry of characteristic functions of the parafermions related to the generalized deformed oscillator of Daskaloyannis et al. The…
A section of a Hamiltonian system is a hypersurface in the phase space of the system, usually representing a set of one-sided constraints (e.g. a boundary, an obstacle or a set of admissible states). In this paper we give local…
We present a method for computing first order asymptotics of semiclassical spectra for 1-D Bogoliubov-de Gennes (BdG) Hamiltonian from Supraconductivity, which models the electron/hole scattering through two SNS junctions. This involves: 1)…
In order to make data-driven models of physical systems interpretable and reliable, it is essential to include prior physical knowledge in the modeling framework. Hamiltonian Neural Networks (HNNs) implement Hamiltonian theory in deep…
We consider quantum many body systems with generalized symmetries, such as the higher form symmetries introduced recently, and the "tensor symmetry". We consider a general form of lattice Hamiltonians which allow a certain level of…
Hybrid machine learning based on Hamiltonian formulations has recently been successfully demonstrated for simple mechanical systems, both energy conserving and not energy conserving. We introduce a pseudo-Hamiltonian formulation that is a…
Higher order normalizations are performed in the generalized photogravitational restricted three body problem with Poynting-Robertson drag. In this problem we have taken bigger primary as a source of radiation and smaller primary as an…
We analyze the class of Generalized Double Semion (GDS) models in arbitrary dimensions from the point of view of lattice Hamiltonians. We show that on a $d$-dimensional spatial manifold $M$ the dual of the GDS is equivalent, up to constant…
In recent work, Baird et al. have generalized the definition of the Maslov index to paths of Grassmannian subspaces that are not necessarily contained in the Lagrangian Grassmannian [T. J. Baird, P. Cornwell, G. Cox, C. Jones, and R.…
While independent observations have been made regarding the behaviour of effective quasinormal mode (QNM) potentials within the large angular momentum limit, we demonstrate analytically here that a uniform expression emerges for…
We demonstrate that a system of bi-orthogonal polynomials and their associated functions corresponding to a regular semi-classical weight on the unit circle constitute a class of general classical solutions to the Garnier systems by…
The paper deals with the problem of the existence of a normal form for a nearly-integrable real-analytic Hamiltonian with aperiodically time-dependent perturbation decaying (slowly) in time. In particular, in the case of an isochronous…
We introduce a new class $\mathbb{G}^n_s$ of generic real analytic potentials on $\mathbb{T}^n$ and study global analytic properties of natural nearly-integrable Hamiltonians $\frac12 |y|^2+\varepsilon f(x)$, with potential $f\in…
Rational normal form is a powerful tool to deal with Hamiltonian partial differential equations without external parameters. In this paper, we build rational normal form with exact global control of small divisors. As an application to…
In this paper, separability of the perturbed two-dimensional isotropic harmonic oscillators with homogeneous polynomial potentials is characterized from their Birkhoff-Gustavson (BG) normalization, one of the conventional methods for…
In this work we consider a saddle-center equilibrium for general vector fields as well as Hamiltonian systems, and we transform it locally into a polynomial normal form in the saddle variables by a change of coordinates. This problem was…
The Lagrangian-Hamiltonian unified formalism of R. Skinner and R. Rusk was originally stated for autonomous dynamical systems in classical mechanics. It has been generalized for non-autonomous first-order mechanical systems, as well as for…