27 citations · 127 across the 32 of their papers we have counts for
16 papers · 1 filter
Hamiltonian reduction from particular integrals
R. Azuaje, A. M. Escobar-Ruiz, I. Gutierrez-Sagredo
We develop a geometric reduction mechanism generated by systems of particular integrals, namely, families of functions whose time derivatives close linearly on the family. Their co…
Nonlinear Lissajous orbits and particular superintegrability
A. M. Escobar-Ruiz, R. Azuaje
We investigate the geometry of classical trajectories generated by separable two-dimensional polynomial potentials of the form , wher…
Superintegrability and choreographic obstructions in dihedral -body Hamiltonian systems
A M Escobar-Ruiz, M Fernandez-Guasti
We study planar -body Hamiltonians with quadratic pair interactions whose coupling pattern is invariant under the dihedral group . After the center of mass is removed, the…
Two-dimensional classical superintegrable systems: polynomial algebra of integrals
A. M. Escobar-Ruiz, R. Azuaje, J. C. Gordiano
In this work, we investigate generic classical two-dimensional (2D) superintegrable Hamiltonian systems H, characterized by the existence of three functionally independent integral…
On the four-body limaçon choreography: maximal superintegrability and choreographic fragmentation
Adrian M Escobar-Ruiz, Manuel Fernandez-Guasti
In this paper, as a continuation of [Fernandez-Guasti, \textit{Celest Mech Dyn Astron} 137, 4 (2025)], we demonstrate the maximal superintegrability of the reduced Hamiltonian, whi…
Canonical transformations: from the coordinate based approach to the geometric one
R. Azuaje, A. M. Escobar-Ruiz
In this paper the theory of time-dependent and time-independent canonical transformations is considered from a geometric perspective. Both the geometric formalism and the coordinat…
Two-body Coulomb problem and hidden algebra: superintegrability and cubic polynomial algebra
Alexander V. Turbiner, Adrian M. Escobar-Ruiz
It is shown that the two-body Coulomb problem in the Sturm representation leads to a new two-dimensional, exactly-solvable, superintegrable quantum system in curved space with a $g…
On particular integrability in classical mechanics
A. M. Escobar-Ruiz, R. Azuaje
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 symplect…
Canonical and canonoid transformations for Hamiltonian systems on (co)symplectic and (co)contact manifolds
R. Azuaje, A. M. Escobar-Ruiz
In this paper we present canonical and canonoid transformations considered as global geometrical objects for Hamiltonian systems. Under the mathematical formalisms of symplectic, c…
Classical -body system in geometrical and volume variables. I. Three-body case
A. M. Escobar-Ruiz, R. Linares, Alexander V Turbiner +1
We consider the classical 3-body system with degrees of freedom at zero total angular momentum. The study is restricted to potentials that depend solely on relative…
The spin representations via sigma models
P. P. Goldstein, A. M. Grundland, A. M. Escobar Ruiz
We establish and analyze a new relationship between the matrices describing an arbitrary component of a spin , where , and the matrices of …
New infinite families of th-order superintegrable systems separating in Cartesian coordinates
A. M. Escobar-Ruiz, R. Linares, P. Winternitz
A study is presented of superintegrable quantum systems in two-dimensional Euclidean space allowing the separation of variables in Cartesian coordinates. In addition to the H…
General -order superintegrable systems separating in polar coordinates
A. M. Escobar-Ruiz, P. Winternitz, I. Yurdusen
The general description of superintegrable systems with one polynomial integral of order in the momenta is presented for a Hamiltonian system in two-dimensional Euclidean plane…
Fourth-order superintegrable systems separating in Polar Coordinates. II. Standard Potentials
A. M. Escobar-Ruiz, J. C. López Vieyra, P. Winternitz +1
Superintegrable Hamiltonian systems in a two-dimensional Euclidean space are considered. We present all real standard potentials that allow separation of variables in polar coordin…
Fourth order superintegrable systems separating in Polar Coordinates. I. Exotic Potentials
Adrian M. Escobar-Ruiz, J. C. López Vieyra, P. Winternitz
We present all real quantum mechanical potentials in a two-dimensional Euclidean space that have the following properties: 1. They allow separation of variables of the Schrödinger…
Three-body problem in 3D space: ground state, (quasi)-exact-solvability
Alexander V Turbiner, Willard Miller, Adrian M Escobar-Ruiz
We study aspects of the quantum and classical dynamics of a -body system in 3D space with interaction depending only on mutual distances. The study is restricted to solutions in…