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.
Highlights
We consider two degree of freedom integrable Hamiltonian systems defined by two Poisson commuting functions F1, F2 on a symplectic manifold (P, ω)
The rotation number depends on the dynamics its variation along a path Γ depends only on the geometry of the fibration. This remains true for fractional monodromy provided that, F is chosen in such a way so that the rotation number does not diverge when Γ crosses the curve C of critical values of F so that the variation is well defined
We have showed that in 2 degree of freedom integrable Hamiltonian systems with curled tori and a global S1 action we have fractional monodromy
Summary
We consider two degree of freedom integrable Hamiltonian systems defined by two Poisson commuting functions F1, F2 on a symplectic manifold (P, ω). There exists in Vjc a local smooth two dimensional Poincare section Σlocal to the critical orbit oc such that the return map is the time π flow of XJ .
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
