Three and four-body systems in one dimension: integrability, superintegrability and discrete symmetries
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Publication:2341139
DOI10.1134/S1560354711050066zbMath1309.70021arXiv0907.5288MaRDI QIDQ2341139
Luca Degiovanni, Claudia Maria Chanu, Giovanni Rastelli
Publication date: 23 April 2015
Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0907.5288
discrete symmetriessuperintegrabilityhigher-degree first integralsTremblay-Turbiner-Winterniz system
Three-body problems (70F07) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) (n)-body problems (70F10)
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Cites Work
- First integrals of extended Hamiltonians in \(n+1\) dimensions generated by powers of an operator
- Tools for verifying classical and quantum superintegrability
- Multiparticle systems. The algebra of integrals and integrable cases
- Leonard Euler: addition theorems and superintegrable systems
- Superintegrable system on a sphere with the integral of higher degree
- On algebraic construction of certain integrable and super-integrable systems
- Hidden symmetries of integrable conformal mechanical systems
- The super-separability of the three-body inverse-square Calogero system
- Necessary conditions for classical super-integrability of a certain family of potentials in constant curvature spaces
- Superintegrable three-body systems on the line
- The cuboctahedric Higgs oscillator from the rational Calogero model
- An infinite family of solvable and integrable quantum systems on a plane
- Polynomial constants of motion for Calogero-type systems in three dimensions
- Families of classical subgroup separable superintegrable systems
- Periodic orbits for an infinite family of classical superintegrable systems
