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SUMMARY:Monodromy of analytic continuation of Birkhoff normal forms for fr
 ee rigid body dynamics and an elliptic fibration
DTSTART:20141215T153000
DTEND:20141215T163000
DTSTAMP:20260428T044240Z
UID:08ed74843c247d0e191e46a877ef1420cc29515e4ea0fae00213e544
CATEGORIES:Conferences - Seminars
DESCRIPTION:Daisuke Tarama (Kyoto)\nGeometry and Dynamics Seminar\nAbstrac
 t: The Birkhoff normal form is a power series expansion of the Hamiltonian
  associated with the local behavior of a Hamiltonian system near a critica
 l point.\nIt is known that around the critical point one can take a conver
 gent canonical transformation which puts the Hamiltonian into Birkhoff nor
 mal form for integrable systems under some non-degeneracy conditions.\nIn 
 this talk\, analytic continuation of the Birkhoff normal forms is consider
 ed for the (complexified) free rigid body dynamics on SO(3)\, by means of 
 an expression of the derivative for the inverse of Birkhoff normal form by
  a period integral. It is shown that the monodromy of the analytic continu
 ation for the derivative of the inverse for the Birkhoff normal forms coin
 cides with that of an elliptic fibration which naturally arises from the d
 ynamics. Further\, the global monodromy is concretely calculated as a repr
 esentation of a colored braid group.\nThis talk is based on a joint work w
 ith Jean-Pierre Françoise (LJLL-UPMC).
LOCATION:MA A1 10
STATUS:CONFIRMED
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