Singularities of Whitham flows for hyperelliptic spectral curves
Dynamical Systems
2017-09-11 v2 Differential Geometry
Abstract
We consider the Whitham equations for deformations of hyperelliptic spectral curves, which preserve all periods of a meromorphic differential. If the meromorphic differential has a root at a fixed point of the hyperelliptic involution, then the Whitham flow has a singularity. We prove that the stable and unstable manifolds are non-empty and extend the Whitham flow continuously through the singularity.
Keywords
Cite
@article{arxiv.1709.02330,
title = {Singularities of Whitham flows for hyperelliptic spectral curves},
author = {Laurent Hauswirth and Martin Kilian and Martin U. Schmidt},
journal= {arXiv preprint arXiv:1709.02330},
year = {2017}
}
Comments
16 pages, no figures