Extended Hamilton–Jacobi Theory, Symmetries and Integrability by Quadratures

Symmetries and Integrability

This is a survey on finite-dimensional integrable dynamical systems related to Hamiltonian G-actions. Within a framework of noncommutative integrability we study integrability of G-invariant systems, collective motions and reduced integrability. We also consider reductions of the Hamiltonian flows restricted to their invariant submanifolds generalizing classical Hess–Appel’rot case of a heavy r...

Incompleteness of Representation Theory: Hidden symmetries and Quantum Non-Integrability

When regular regions are discovered in the parameter space of a system, where the parameter might be an external field applied to the Hydrogen atom, it usually indicates the existence of new (approximate) integrals of motion, and consequently quantum numbers [1]. In studies of many–body systems, the large number of degrees of freedom generally precludes one from using methods introduced in simp...

Preface: Symmetries and Integrability of Difference Equations

Preface: Symmetries and Integrability of Difference Equations

Null Kähler structures, Symmetries and Integrability

I feel honoured to be able to make this small contribution to the celebration of Jerzy Plebański’s 75th birthday. Plebański has presumably regarded his work on complex relativity as a step towards producing general solutions to the Einstein equations on a real Lorentzian manifold. No one in the mid-seventies could expect that his contributions to the field would underlie the relation between tw...