Curvature as an Integrable Deformation
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Publication:4973353
DOI10.1007/978-3-030-20087-9_1zbMath1428.70034arXiv1903.09543OpenAlexW2923871673MaRDI QIDQ4973353
Alfonso Blasco, Ángel Ballesteros, Francisco J. Herranz
Publication date: 3 December 2019
Published in: Integrability, Supersymmetry and Coherent States (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1903.09543
sphereintegrable systemscurvatureintegrable perturbationshyperbolic planeHénon-Heilesoscillator potential
Groups and algebras in quantum theory and relations with integrable systems (81R12) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06)
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Cites Work
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- There is a projective dynamics
- Dynamical algebras of general two-parametric Pöschl-Teller Hamiltonians
- The \(n\)-body problem in spaces of constant curvature. II: Singularities
- Projective dynamics and first integrals
- An exactly solvable deformation of the Coulomb problem associated with the Taub-NUT metric
- Superintegrable systems on spaces of constant curvature
- A unified approach to quantum and classical TTW systems based on factorizations
- A family of exactly solvable radial quantum systems on space of non-constant curvature with accidental degeneracy in the spectrum
- Superintegrable oscillator and Kepler systems on spaces of nonconstant curvature via the Stäckel transform
- An extended Hénon-Heiles system
- Quantum mechanics on spaces of nonconstant curvature: the oscillator problem and superintegrability
- Homographic solutions of the curved 3-body problem
- Integrable Hénon-Heiles hamiltonians: a Poisson algebra approach
- Completeness of the cubic and quartic Hénon-Heiles hamiltonians
- Extended Hamiltonians, coupling-constant metamorphosis and the Post-Winternitz system
- Harmonic oscillator on the \(\mathrm{SO}(2,2)\) hyperboloid
- The Kepler problem and the Laplace-Runge-Lenz vector on spaces of constant curvature and arbitrary signature
- Superintegrability on \(N\)-dimensional curved spaces: central potentials, centrifugal terms and monopoles
- Hamiltonian systems admitting a Runge-Lenz vector and an optimal extension of Bertrand's theorem to curved manifolds
- The Hénon-Heiles system revisited
- Separable Hamiltonians and integrable systems of hydrodynamic type
- Group approach to the factorization of the radial oscillator equation
- Integrable problems of celestial mechanics in spaces of constant curvature.
- The Post-Winternitz system on spherical and hyperbolic spaces: a proof of the superintegrability making use of complex functions and a curvature-dependent formalism
- The anisotropic oscillator on curved spaces: a exactly solvable model
- On some properties of harmonic oscillator on spaces of constant curvature.
- The quantum harmonic oscillator on the sphere and the hyperbolic plane
- Factorizations of one-dimensional classical systems
- A maximally superintegrable system on an \(n\)-dimensional space of nonconstant curvature
- Superintegrability on three-dimensional Riemannian and relativistic spaces of constant curvature
- Completeness of superintegrability in two-dimensional constant-curvature spaces
- Integrable anharmonic oscillators on spheres and hyperbolic spaces
- Classical and quantum superintegrability with applications
- Relative equilibria in the 3-dimensional curved n-body problem
- On the integrability of stationary and restricted flows of the KdV hierarchy
- A new integrable anisotropic oscillator on the two-dimensional sphere and the hyperbolic plane
- An integrable hierarchy with a perturbed Hénon–Heiles system
- Universal integrals for superintegrable systems on N-dimensional spaces of constant curvature
- An integrable Hénon–Heiles system on the sphere and the hyperbolic plane
- The Jordan–Schwinger representations of Cayley–Klein groups. I. The orthogonal groups
- Bertrand spacetimes as Kepler/oscillator potentials
- Maximal superintegrability of the generalized Kepler–Coulomb system onN-dimensional curved spaces
- Dynamical symmetries in a spherical geometry. I
- Dynamical symmetries in a spherical geometry. II
- Analytic structure of the Henon–Heiles Hamiltonian in integrable and nonintegrable regimes
- Group theory of the Smorodinsky–Winternitz system
- New aspects of integrability of generalized Henon-Heiles systems
- Separability and Lax pairs for Hénon–Heiles system
- Quantum structure of the motion groups of the two-dimensional Cayley-Klein geometries
- Integrability, Stäckel spaces, and rational potentials
- Maximal superintegrability onN-dimensional curved spaces
- Conformal symmetries of spacetimes
- Superintegrable systems on the two-dimensional sphere S2 and the hyperbolic plane H2
- Trigonometry of spacetimes: a new self-dual approach to a curvature/signature (in)dependent trigonometry
- Completeness of multiseparable superintegrability on the complex 2-sphere
- A non-linear oscillator with quasi-harmonic behaviour: two- andn-dimensional oscillators
- Superintegrability in three-dimensional Euclidean space
- On harmonic oscillators on the two-dimensional sphere S2 and the hyperbolic plane H2
- Superintegrability in a two-dimensional space of nonconstant curvature
- Commensurate harmonic oscillators: Classical symmetries
- On harmonic oscillators on the two-dimensional sphere S2 and the hyperbolic plane H2. II.
- Cayley-Klein algebras as graded contractions of so(N+1)
- The anisotropic oscillator on the 2D sphere and the hyperbolic plane
- Superintegrable deformations of superintegrable systems: Quadratic superintegrability and higher-order superintegrability
- Generalized MICZ-Kepler system, duality, polynomial, and deformed oscillator algebras
- Three-Dimensional Isotropic Harmonic Oscillator and SU3
- The Tremblay–Turbiner–Winternitz system on spherical and hyperbolic spaces: superintegrability, curvature-dependent formalism and complex factorization
- Superintegrability on curved spaces, orbits and momentum hodographs: revisiting a classical result by Hamilton
- Anisotropic inharmonic Higgs oscillator and related (MICZ-)Kepler-like systems
- Superintegrability of the caged anisotropic oscillator
- Integrable potentials on spaces with curvature from quantum groups
- On the Problem of Degeneracy in Quantum Mechanics
- On the Contraction of Groups and Their Representations
- Painleve analysis and integrability of coupled non-linear Schrodinger equations
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