An atlas adapted to the Toda flow
arXiv:1909.02676
Abstract
We introduce an atlas adapted to the Toda flow on the manifold of full flags of any non-compact real semisimple Lie algebra, and on its Hessenberg-type submanifolds. In our local coordinates the Toda flow becomes linear. We use these new coordinates to show that the Toda flow on the manifold of full flags is Morse-Smale, which generalizes the main result of \cite{CSS1} to arbitrary non-compact real semisimple Lie algebras. As a byproduct we describe new features of classical constructions in matrix theory.
Changes regarding the different manifolds associated to Hessenberg-type data and modifications in the presentation