27 citations · 127 across the 32 of their papers we have counts for
32 papers
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…
Nodal algebraic curves and entropy diagnostics in degenerate two-dimensional harmonic-oscillator shells
C A Escobar Ruiz, H Olivares-Pilon, A M Escobar-Ruiz
Degeneracy allows the nodal structure of a quantum state to vary without changing its energy. We study this effect for real superpositions in the fixed-energy shells of the two-dim…
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…
Cylindrically confined atom in magnetic field: variational cut-off factor
A. N. Mendoza Tavera, H. Olivares-Pilón, M. Rodríguez-Arcos +1
In the present study, we consider the hydrogen atom confined within an impenetrable infinite cylindrical cavity of radius in the presence of a constant magnetic field ${\bf…
Exploring the Multifractal Behavior of the Human Genome T2T-CHM13v2.0: Graphical Representations and Cytogenetics
Yulián A. Alvarez-Ballesteros, Mario A. Quiroz-Juarez, José L. Del-Rio-Correa +1
In this work, we applied the Chaos Game Representation (CGR) to the complete human genomic sequence T2T-CHM13v2.0, analyzing the entire chromosome assembly and each chromosome sepa…
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…
The QES sextic and Morse potentials: exact WKB condition and supersymmetry
Alonso Contreras-Astorga, A. M. Escobar-Ruiz
In this paper, as a continuation of [Contreras-Astorga A., Escobar-Ruiz A. M. and Linares R., \textit{Phys. Scr.} {\bf99} 025223 (2024)] the one-dimensional quasi-exactly solvable…
Data-driven reconstruction of chaotic dynamical equations: the Hénon-Heiles type system
A. M. Escobar-Ruiz, L. Jiménez-Lara, P. M. Juárez-Florez +3
In this study, the classical two-dimensional potential , , is considered. At , the system i…
The SUSY partners of the QES sextic potential revisited
Alonso Contreras-Astorga, A. M. Escobar-Ruiz, Román Linares
In this paper, the SUSY partner Hamiltonians of the quasi-exactly solvable (QES) sextic potential …
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…
Equivalence classes and Linearization of the Riccati and Abel chain
J. C. Ndogmo, Adrian M. Escobar-Ruiz
The problem of linearization by point transformations is solved for equations in the generalized Riccati and Abel chain of order not exceeding the fourth. It is shown in particular…
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…
3-body harmonic molecule
H. Olivares-Pilón, A. M. Escobar-Ruiz, F. Montoya
In this study, the quantum 3-body harmonic system with finite rest length and zero total angular momentum is explored. It governs the near-equilibrium -states eigenfun…
Classical -body system in volume variables. II. Four-body case
A. M. Escobar-Ruiz, Alexander V Turbiner
It is evident that the positions of 4 bodies in dimensional space can be identified with vertices of a tetrahedron. Square of volume of the tetrahedron, weighted sum of squar…
Hydrogen atom confined inside an inverted-Gaussian potential
H. Olivares-Pilón, A. M. Escobar-Ruíz, M. A. Quiroz-Juárez +1
In this work, we consider the hydrogen atom confined inside a penetrable spherical potential. The confining potential is described by an inverted-Gaussian function of depth ,…
Testing the scalar sector of the Standard-Model Extension with neutron gravity experiments
C. A. Escobar, A. Martín-Ruiz, A. M. Escobar-Ruiz +1
In the present study we analyse, within the scalar sector of the Standard-Model Extension (SME) framework, the influence of a spontaneous Lorentz symmetry breaking on gravitational…
Classical harmonic three-body system: An experimental electronic realization
A. M. Escobar-Ruiz, M. A. Quiroz-Juarez, J. L. Del Rio-Correa +1
The classical three-body harmonic system in () with finite rest lengths and zero total angular momentum is considered. This model describes the dynamics o…
Doubly Exotic th-order Order Superintegrable Classical Systems Separating in Cartesian Coordinates
İsmet Yurduşen, Adrián Mauricio Escobar-Ruiz, Irlanda Palma y Meza Montoya
Superintegrable classical Hamiltonian systems in two-dimensional Euclidean space are explored. The study is restricted to Hamiltonians allowing separation of variables $V(x,y…
Helium-like ions in -dimensions: analyticity and generalized ground state Majorana solutions
Adrian M. Escobar-Ruiz, Horacio Olivares-Pilón, Norberto Aquino +1
Non-relativistic Helium-like ions with static nucleus in a dimensional space () are considered. Assuming Coulomb interactions, a 2-par…
Scalar Casimir effect for a conducting cylinder in a Lorentz violating background
A. M. Escobar-Ruiz, A. Martín-Ruiz, Escobar C. A. +1
Following a field-theoretical approach, we study the scalar Casimir effect upon a perfectly conducting cylindrical shell in the presence of spontaneous Lorentz symmetry breaking. T…