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arXiv · 1609.07003

Parallel transport along Seifert manifolds and fractional monodromy

N. Martynchuk·K. Efstathiou
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Abstract

The notion of fractional monodromy was introduced by Nekhoroshev, Sadovskií and Zhilinskií 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.

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N. Martynchuk, K. Efstathiou. 2017-10-02. Parallel transport along Seifert manifolds and fractional monodromy. https://doi.org/10.1007/s00220-017-2988-5

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