5 problems

Let ${\cal H}_\kappa$ be the curved anisotropic oscillator Hamiltonian depending on the parameters $(\Omega_1,\Omega_2)$. Numerical integration finds closed trajectories only for…

Let a Euclidean anisotropic oscillator have commensurate frequencies, so that it is superintegrable. A curved-generalization conjecture. Each Euclidean superintegrable anisotropic…

Let $m:n$ be a commensurate frequency ratio for a Euclidean anisotropic oscillator. A curved integrable-family conjecture. For each such commensurate, and hence superintegrable, Eu…

Let ${\cal H}_\kappa$ denote the curved anisotropic oscillator Hamiltonian on the two-dimensional sphere or hyperbolic plane, with anisotropy parameter $\Omega$; the Euclidean limi…

Let ${\cal H}_\kappa$ be the curved Hamiltonian on the two-dimensional sphere, hyperbolic plane, or Euclidean plane, with constant Gaussian curvature $\kappa$, anisotropy parameter…