The Tremblay-Turbiner-Winternitz system as extended Hamiltonian
From MaRDI portal
Publication:2939227
DOI10.1063/1.4903508zbMath1308.70021arXiv1404.4825OpenAlexW3102212039MaRDI QIDQ2939227
Luca Degiovanni, Giovanni Rastelli, Claudia Maria Chanu
Publication date: 19 January 2015
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1404.4825
Hamilton's equations (70H05) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06)
Related Items
Born-Jordan and Weyl quantizations of the 2D anisotropic harmonic oscillator ⋮ Doubly exotic \(N\)th-order superintegrable classical systems separating in Cartesian coordinates ⋮ Extended Hamiltonians and shift, ladder functions and operators ⋮ Separation of variables and superintegrability on Riemannian coverings ⋮ On the extended-Hamiltonian structure of certain superintegrable systems on constant-curvature Riemannian and pseudo-Riemannian surfaces ⋮ Quasi-bi-Hamiltonian structures, complex functions and superintegrability: the Tremblay–Turbiner–Winternitz (TTW) and the Post–Winternitz (PW) systems ⋮ Modified Laplace-Beltrami quantization of natural Hamiltonian systems with quadratic constants of motion ⋮ Extensions of nonnatural Hamiltonians ⋮ Superintegrability on the three-dimensional spaces with curvature. Oscillator-related and Kepler-related systems on the sphere S 3 and on the hyperbolic space H 3
Cites Work
- Superintegrable extensions of superintegrable systems
- First integrals of extended Hamiltonians in \(n+1\) dimensions generated by powers of an operator
- Tools for verifying classical and quantum superintegrability
- Superintegrable system on a sphere with the integral of higher degree
- Classical and quantum superintegrability with applications
- Extensions of Hamiltonian systems dependent on a rational parameter
- Chiral super-Tremblay–Turbiner–Winternitz Hamiltonians and their dynamical superalgebra
- Necessary conditions for classical super-integrability of a certain family of potentials in constant curvature spaces
- Superintegrable three-body systems on the line
- An infinite family of solvable and integrable quantum systems on a plane
- Superintegrable systems on the two-dimensional sphere S2 and the hyperbolic plane H2
- Polynomial constants of motion for Calogero-type systems in three dimensions
- The Tremblay–Turbiner–Winternitz system on spherical and hyperbolic spaces: superintegrability, curvature-dependent formalism and complex factorization
