Related papers: Note on integrability of certain homogeneous Hamil…
In this work we compute the families of classical Hamiltonians in two degrees of freedom in which the Normal Variational Equation around an invariant plane falls in Schroedinger type with polynomial or trigonometrical potential. We analyze…
The difference variational bicomplex, which is the natural setting for systems of difference equations, is constructed and used to examine the geometric and algebraic properties of various systems. Exactness of the bicomplex gives a…
We study the integrability in the Liouville sense of natural Hamiltonian systems with a homogeneous rational potential $V(\vq)$. Strong necessary conditions for the integrability of such systems were obtained by an analysis of differential…
The Hamilton-Jacobi problem is revisited bearing in mind the consequences arising from a possible bi-Hamiltonian structure. The problem is formulated on the tangent bundle for Lagrangian systems in order to avoid the bias of the existence…
We prove two statements about the long time dynamics of integrable Hamiltonian systems. In classical mechanics, we prove the microcanonical version of the Generalized Gibbs Ensemble (GGE) by mapping it to a known theorem and then extend it…
Gyrokinetic field theory is addressed in the context of a general Hamiltonian. The background magnetic geometry is static and axisymmetric, and all dependence of the Lagrangian upon dynamical variables is in the Hamiltonian or in free field…
This is an example of application of Ziglin-Morales-Ramis algebraic studies in Hamiltonian integrability, more specifically the result by Morales, Ramis and Sim\'o on higher-order variational equations, to the well-known…
It is believed that thermodynamic laws are associated with random processes occurring in the system and, therefore, deterministic mechanical systems cannot be described within the framework of the thermodynamic approach. In this paper, we…
Described is n-level quantum system realized in the n-dimensional ''Hilbert'' space H with the scalar product G taken as a dynamical variable. The most general Lagrangian for the wave function and G is considered. Equations of motion and…
A class of fast-slow Hamiltonian systems with potential $U_\varepsilon$ describing the interaction of non-ergodic fast and slow degrees of freedom is studied. The parameter $\varepsilon$ indicates the typical timescale ratio of the fast and…
A complex quantum system with energy dissipation is considered. The quantum Hamiltonians $H$ belong the complex Ginibre ensemble. The complex-valued eigenenergies $Z_{i}$ are random variables. The second differences $\Delta^{1} Z_{i}$ are…
We investigate the Liouvillian integrability of Hamiltonian systems describing a universe filled with a scalar field (possibly complex). The tool used is the differential Galois group approach, as introduced by Morales-Ruiz and Ramis. The…
We derived a condition under which a coupled system consisting of two finite-dimensional Hamiltonian systems becomes a Hamiltonian system. In many cases, an industrial system can be modeled as a coupled system of some subsystems. Although…
We derive a system with one degree of freedom that models a class of dynamical systems with strange attractors in three dimensions. This system retains all the characteristics of chaotic attractors and is expressed by a second-order…
Integrability conditions for systems of bosons or fermions with seniority conserving hamiltonians are derived. The conditions are shown to be invariant under a large class of transformations of the interaction matrix elements. Previously…
Phase space of a characteristic Hamiltonian system is a symplectic leaf of a factorizable Poisson Lie group. Its Hamiltonian is a restriction to the symplectic leaf of a function on the group which is invariant with respect to conjugations.…
The main purpose of this paper is to introduce a new class of Hamiltonian scattering systems of the cone potential type that can be integrated via the asymptotic velocity. For a large subclass, the asymptotic data of the trajectories define…
In this paper we analyze the normal forms of a general quadratic Hamiltonian system defined on the dual of the Lie algebra $\mathfrak{o}(K)$ of real $K$ - skew - symmetric matrices, where $K$ is an arbitrary $3\times 3$ real symmetric…
We study several aspects of the regular deformations of completely integrable systems. Namely, we prove the existence of a Hamiltonian normal form for these deformations and we show the necessary and sufficient conditions a perturbation has…
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…