Conjectures that for integer k the TTW Hamiltonian H and integrals I1, I2, I12 generate a polynomial algebra of order k+1 inside hidden algebra g^(k), verified explicitly for k=1 to 4.
Turbiner, From quantumA N (Sutherland) toE 8 trigonometric model: space-of-orbits view, SIGMA9, 003 (2013)
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Tremblay-Turbiner-Winternitz (TTW) system at integer index $k$: polynomial algebras of integrals
Conjectures that for integer k the TTW Hamiltonian H and integrals I1, I2, I12 generate a polynomial algebra of order k+1 inside hidden algebra g^(k), verified explicitly for k=1 to 4.