Asymptotics of action variables near semi-toric singularities

The presence of focus-focus singularities in semi-toric integrables Hamiltonian systems is one of the reasons why there cannot exist global Action-Angle coordinates on such systems. At focus-focus critical points, the Liouville-Arnold-Mineur theorem does not apply. In particular, the affine structure of the image of the moment map around has non-trivial monodromy. In this article, we establish that the singular behavior and the multivaluedness of the Action integrals is given by a complex logarithm. This extends a previous result by San VU Ngoc to any dimension. We also calculate the monodromy matrix for these systems. (C) 2015 Elsevier B.V. All rights reserved.


Published in:
Journal Of Geometry And Physics, 98, 28-39
Year:
2015
Publisher:
Amsterdam, Elsevier
ISSN:
0393-0440
Keywords:
Laboratories:




 Record created 2016-02-16, last modified 2018-01-28


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