224 citations · 2.5k across the 74 of their papers we have counts for
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A class of solvable Lie algebras and their Casimir Invariants
L. Snobl, P. Winternitz
A nilpotent Lie algebra n_{n,1} with an (n-1) dimensional Abelian ideal is studied. All indecomposable solvable Lie algebras with n_{n,1} as their nilradical are obtained. Their di…
Periodicity and Quasi-Periodicity for Super-Integrable Hamiltonian Systems
Maurice Robert Kibler, Pavel Winternitz
Classical trajectories are calculated for two Hamiltonian systems with ring shaped potentials. Both systems are super-integrable, but not maximally super-integrable, having four gl…
Subgroup type coordinates and the separation of variables in Hamilton-Jacobi and Schrődinger equations
E. G. Kalnins, Z. Thomova, P. Winternitz
Separable coordinate systems are introduced in the complex and real four-dimensional flat spaces. We use maximal Abelian subgroups to generate coordinate systems with a maximal num…
Lie Symmetries and Exact Solutions of First Order Difference Schemes
Miguel A. Rodriguez, Pavel Winternitz
We show that any first order ordinary differential equation with a known Lie point symmetry group can be discretized into a difference scheme with the same symmetry group. In gener…