Parallel transport along Seifert manifolds and fractional monodromy
Mathematical Physics
2017-10-03 v2 math.MP
Abstract
The notion of fractional monodromy was introduced by Nekhoroshev, Sadovski\'{i} and Zhilinski\'{i} as a generalization of standard (`integer') monodromy in the sense of Duistermaat from torus bundles to singular torus fibrations. In the present paper we prove a general result that allows to compute fractional monodromy in various integrable Hamiltonian systems. In particular, we show that the non-triviality of fractional monodromy in 2 degrees of freedom systems with a Hamiltonian circle action is related only to the fixed points of the circle action. Our approach is based on the study of a specific notion of parallel transport along Seifert manifolds.
Keywords
Cite
@article{arxiv.1609.07003,
title = {Parallel transport along Seifert manifolds and fractional monodromy},
author = {N. Martynchuk and K. Efstathiou},
journal= {arXiv preprint arXiv:1609.07003},
year = {2017}
}