Symmetries and integrability

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...

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...

Black holes, hidden symmetries, and complete integrability

The study of higher-dimensional black holes is a subject which has recently attracted vast interest. Perhaps one of the most surprising discoveries is a realization that the properties of higher-dimensional black holes with the spherical horizon topology and described by the Kerr-NUT-(A)dS metrics are very similar to the properties of the well known four-dimensional Kerr metric. This remarkable...