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Curvature as an Integrable Deformation (Q4973353)

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scientific article; zbMATH DE number 7139471

Language	Label	Description	Also known as
English	Curvature as an Integrable Deformation	scientific article; zbMATH DE number 7139471

Statements

scholarly article

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Curvature as an Integrable Deformation (English)

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Ángel Ballesteros

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Francisco J. Herranz

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Integrability, Supersymmetry and Coherent States

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publication date

3 December 2019

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full work available at URL

https://arxiv.org/abs/1903.09543

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zbMATH Keywords

integrable systems

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curvature

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sphere

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hyperbolic plane

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integrable perturbations

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oscillator potential

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Hénon-Heiles

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MaRDI profile type

MaRDI publication profile

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Integrable problems of celestial mechanics in spaces of constant curvature.

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Classical and quantum superintegrability with applications

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Quantum structure of the motion groups of the two-dimensional Cayley-Klein geometries

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Superintegrable systems on the two-dimensional sphere S2 and the hyperbolic plane H2

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Trigonometry of spacetimes: a new self-dual approach to a curvature/signature (in)dependent trigonometry

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Conformal symmetries of spacetimes

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On some properties of harmonic oscillator on spaces of constant curvature.

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On harmonic oscillators on the two-dimensional sphere S2 and the hyperbolic plane H2

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Maximal superintegrability on<i>N</i>-dimensional curved spaces

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Superintegrability on three-dimensional Riemannian and relativistic spaces of constant curvature

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Universal integrals for superintegrable systems on N-dimensional spaces of constant curvature

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The quantum harmonic oscillator on the sphere and the hyperbolic plane

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Superintegrability on curved spaces, orbits and momentum hodographs: revisiting a classical result by Hamilton

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The Kepler problem and the Laplace-Runge-Lenz vector on spaces of constant curvature and arbitrary signature

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Maximal superintegrability of the generalized Kepler–Coulomb system on<i>N</i>-dimensional curved spaces

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Homographic solutions of the curved 3-body problem

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The \(n\)-body problem in spaces of constant curvature. II: Singularities

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Relative equilibria in the 3-dimensional curved n-body problem

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Superintegrable systems on spaces of constant curvature

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The Tremblay–Turbiner–Winternitz system on spherical and hyperbolic spaces: superintegrability, curvature-dependent formalism and complex factorization

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The Post-Winternitz system on spherical and hyperbolic spaces: a proof of the superintegrability making use of complex functions and a curvature-dependent formalism

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Superintegrable deformations of superintegrable systems: Quadratic superintegrability and higher-order superintegrability

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Extended Hamiltonians, coupling-constant metamorphosis and the Post-Winternitz system

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There is a projective dynamics

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Projective dynamics and first integrals

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The anisotropic oscillator on the 2D sphere and the hyperbolic plane

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A new integrable anisotropic oscillator on the two-dimensional sphere and the hyperbolic plane

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On the Contraction of Groups and Their Representations

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Cayley-Klein algebras as graded contractions of so(N+1)

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The Jordan–Schwinger representations of Cayley–Klein groups. I. The orthogonal groups

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On the Problem of Degeneracy in Quantum Mechanics

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Commensurate harmonic oscillators: Classical symmetries

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The anisotropic oscillator on curved spaces: a exactly solvable model

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Group approach to the factorization of the radial oscillator equation

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Factorizations of one-dimensional classical systems

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Dynamical algebras of general two-parametric Pöschl-Teller Hamiltonians

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A unified approach to quantum and classical TTW systems based on factorizations

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Superintegrability of the caged anisotropic oscillator

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Superintegrability in three-dimensional Euclidean space

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Three-Dimensional Isotropic Harmonic Oscillator and SU3

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Group theory of the Smorodinsky–Winternitz system

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Dynamical symmetries in a spherical geometry. I

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On harmonic oscillators on the two-dimensional sphere S2 and the hyperbolic plane H2. II.

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Completeness of multiseparable superintegrability on the complex 2-sphere

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Completeness of superintegrability in two-dimensional constant-curvature spaces

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Integrability, Stäckel spaces, and rational potentials

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Integrable anharmonic oscillators on spheres and hyperbolic spaces

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Anisotropic inharmonic Higgs oscillator and related (MICZ-)Kepler-like systems

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Generalized MICZ-Kepler system, duality, polynomial, and deformed oscillator algebras

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Dynamical symmetries in a spherical geometry. II

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A non-linear oscillator with quasi-harmonic behaviour: two- and<i>n</i>-dimensional oscillators

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Superintegrability on \(N\)-dimensional curved spaces: central potentials, centrifugal terms and monopoles

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Analytic structure of the Henon–Heiles Hamiltonian in integrable and nonintegrable regimes

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Painleve analysis and integrability of coupled non-linear Schrodinger equations

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The Hénon-Heiles system revisited

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New aspects of integrability of generalized Henon-Heiles systems

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Separability and Lax pairs for Hénon–Heiles system

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On the integrability of stationary and restricted flows of the KdV hierarchy

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Completeness of the cubic and quartic Hénon-Heiles hamiltonians

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An integrable Hénon–Heiles system on the sphere and the hyperbolic plane

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Separable Hamiltonians and integrable systems of hydrodynamic type

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An integrable hierarchy with a perturbed Hénon–Heiles system

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An extended Hénon-Heiles system

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Integrable Hénon-Heiles hamiltonians: a Poisson algebra approach

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Harmonic oscillator on the \(\mathrm{SO}(2,2)\) hyperboloid

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Superintegrability in a two-dimensional space of nonconstant curvature

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Integrable potentials on spaces with curvature from quantum groups

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A maximally superintegrable system on an \(n\)-dimensional space of nonconstant curvature

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Bertrand spacetimes as Kepler/oscillator potentials

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Hamiltonian systems admitting a Runge-Lenz vector and an optimal extension of Bertrand's theorem to curved manifolds

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A family of exactly solvable radial quantum systems on space of non-constant curvature with accidental degeneracy in the spectrum

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Superintegrable oscillator and Kepler systems on spaces of nonconstant curvature via the Stäckel transform

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Quantum mechanics on spaces of nonconstant curvature: the oscillator problem and superintegrability

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An exactly solvable deformation of the Coulomb problem associated with the Taub-NUT metric

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Identifiers

zbMATH Open document ID

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10.1007/978-3-030-20087-9_1

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:4973353

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