224 citations · 2.5k across the 74 of their papers we have counts for
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First integrals of ordinary difference equations beyond Lagrangian methods
V. Dorodnitsyn, E. Kaptsov, R. Kozlov +1
A new method for finding first integrals of discrete equations is presented. It can be used for discrete equations which do not possess a variational (Lagrangian or Hamiltonian) fo…
Classical and Quantum Superintegrability with Applications
Willard Miller, Sarah Post, Pavel Winternitz
A superintegrable system is, roughly speaking, a system that allows more integrals of motion than degrees of freedom. This review is devoted to finite dimensional classical and qua…
First integrals of ordinary difference equations which do not possess a variational formulation
P. Winternitz, V. Dorodnitsyn, E. Kaptsov +1
The paper presents a new method for finding first integrals of ordinary difference equations which do not possess Lagrangians, nor Hamiltonians. As an example we solve a third orde…
Lie groups and numerical solutions of differential equations: Invariant discretization versus differential approximation
Decio Levi, Pavel Winternitz
We briefly review two different methods of applying Lie group theory in the numerical solution of ordinary differential equations. On specific examples we show how the symmetry pre…