Monodromy of Hamiltonian systems with complexity 1 torus actions

JOURNAL OF GEOMETRY AND PHYSICS

卷:115

Article

Efstathiou, K.¹  Martynchuk, N.¹ 

[1] Univ Groningen, Johann Bernoulli Inst Math & Comp Sci, POB 407, NL-9700 AK Groningen, Netherlands

关键词: Principal bundle;    Curvature form;    Integrable Hamiltonian system;    Monodromy;   

DOI  :  10.1016/j.geomphys.2016.05.014

来源: Elsevier

【 摘 要 】

We consider the monodromy of n-torus bundles in n degree of freedom integrable Hamiltonian systems with a complexity 1 torus action, that is, a Hamiltonian Tn-1 action. We show that orbits with T-1 isotropy are associated to non-trivial monodromy and we give a simple formula for computing the monodromy matrix in this case. In the case of 2 degree of freedom systems such orbits correspond to fixed points of the T-1 action. Thus we demonstrate that, given a Tn-1 invariant Hamiltonian H, it is the Tn-1 action, rather than H, that determines monodromy. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free