# A geometric fractional monodromy theorem

H.W. Broer, K. Efstathiou and O.V. Lukina

Discr. Cont. Dyn. Sys. - Ser. S, **3**(4), pp. 517-532, 2010

DOI: 10.3934/dcdss.2010.3.517

## Abstract

We prove the existence of fractional monodromy for two degree of freedom integrable Hamiltonian systems with one-parameter families of curled tori under certain general conditions. We describe the action coordinates of such systems near curled tori and we show how to compute fractional monodromy using the notion of the rotation number.