相关论文: (Super)integrability from coalgebra symmetry: form…

In a preceding paper we introduced a notion of compatibility between a Jacobi structure and a Riemannian structure on a smooth manifold. We proved that in the case of fundamental examples of Jacobi structures : Poisson structures, contact…

The superposition of the Kepler-Coulomb potential on the 3D Euclidean space with three centrifugal terms has recently been shown to be maximally superintegrable [Verrier P E and Evans N W 2008 J. Math. Phys. 49 022902] by finding an…

The $N$-dimensional quantum Hamiltonian $ \hat{H} = -\frac{\hbar^2 {|\mathbf{q} } | }{2(\eta +| {\mathbf{q}} |)} {\mathbf{\nabla}}^2 - \frac{k}{\eta + |{\mathbf{q}} |} $ is shown to be exactly solvable for any real positive value of the…

Motivated by the time-dependent Hamiltonian dynamics, we extend the notion of Arnold-Liouville and noncommutative integrability of Hamiltonian systems on symplectic manifolds to that on cosymplectic manifolds. We prove a variant of the…

Several aspects of the connection between conserved integrals (invariants) and symmetries are illustrated within a hybrid Lagrangian-Hamiltonian framework for dynamical systems. Three examples are considered: a nonlinear oscillator with…

We construct some new Integrable Systems (IS) both classical and quantum associated with elliptic algebras. Our constructions are partly based on the algebraic integrability mechanism given by the existence of commuting families in skew…

In this paper the quantum integrals of the Hamiltonian of the quantum many-body problem with the interaction potential K/sinh^2(x) (Sutherland operator) are constructed as images of higher Casimirs of the Lie algebra gl(N) under a certain…

This text presents some basic notions in symplectic geometry, Poisson geometry, Hamiltonian systems, Lie algebras and Lie groups actions on symplectic or Poisson manifolds, momentum maps and their use for the reduction of Hamiltonian…

Construction and classification of 2D superintegrable systems (i.e. systems admitting, in addition to two global integrals of motion guaranteeing the Liouville integrability, the third global and independent one) defined on 2D spaces of…

We describe a method for determining a complete set of integrals for a classical Hamiltonian that separates in orthogonal subgroup coordinates. As examples, we use it to determine complete sets of integrals, polynomial in the momenta, for…

Bifibrations, in symplectic geometry called also dual pairs, play a relevant role in the theory of superintegrable Hamiltonian systems. We prove the existence of an analogous bifibrated geometry in dynamical systems with a symmetry group…

In this paper we analyze the structure of some subalgebras of quantized enveloping algebras corresponding to unipotent and solvable subgroups of a simple Lie group G. These algebras have the non--commutative structure of iterated algebras…

In this study the notion of particular integrability in Classical Mechanics, introduced in [J. Phys. A: Math. Theor. 46 025203, 2013], is revisited within the formalism of symplectic geometry. A particular integral $\cal I$ is a function…

In this paper, we first recall the notion of (noncommutative) Poisson conformal algebras and describe some constructions of them. Then we study the formal distribution (noncommutative) Poisson algebras and coefficient (noncommutative)…

We propose a unified description for the constants of motion for superintegrable deformations of the oscillator and Coulomb systems on N-dimensional Euclidean space, sphere and hyperboloid. We also consider the duality between these…

Connecting ideas of geometric formulation of quantum mechanics with new results in symplectic geometry a new approach to geometrical quantization procedure is proposed. As a first result we verify that the correspondence between "classical"…

In this paper, we derive a "hamiltonian formalism" for a wide class of mechanical systems, including classical hamiltonian systems, nonholonomic systems, some classes of servomechanism... This construction strongly relies in the geometry…

We introduce a new superintegrable Kepler-Coulomb system with non-central terms in $N$-dimensional Euclidean space. We show this system is multiseparable and allows separation of variables in hyperspherical and hyperparabolic coordinates.…

These notes present an introduction to an analytic version of deformation quantization. The central point is to study algebras of physical observables and their irreducible representations. In classical mechanics one deals with real Poisson…

We discuss, within the simplified context provided by the polymeric harmonic oscillator, a construction leading to a separable Hilbert space that preserves some of the most important features of the spectrum of the Hamiltonian operator.…