Monodromy of analytic continuation of Birkhoff normal forms for free rigid body dynamics and an elliptic fibration
Event details
| Date | 15.12.2014 |
| Hour | 15:30 › 16:30 |
| Speaker | Daisuke Tarama (Kyoto) |
| Location |
MA A1 10
|
| Category | Conferences - Seminars |
Geometry and Dynamics Seminar
Abstract: The Birkhoff normal form is a power series expansion of the Hamiltonian associated with the local behavior of a Hamiltonian system near a critical point.
It is known that around the critical point one can take a convergent canonical transformation which puts the Hamiltonian into Birkhoff normal form for integrable systems under some non-degeneracy conditions.
In this talk, analytic continuation of the Birkhoff normal forms is considered 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 continuation for the derivative of the inverse for the Birkhoff normal forms coincides with that of an elliptic fibration which naturally arises from the dynamics. Further, the global monodromy is concretely calculated as a representation of a colored braid group.
This talk is based on a joint work with Jean-Pierre Françoise (LJLL-UPMC).
Abstract: The Birkhoff normal form is a power series expansion of the Hamiltonian associated with the local behavior of a Hamiltonian system near a critical point.
It is known that around the critical point one can take a convergent canonical transformation which puts the Hamiltonian into Birkhoff normal form for integrable systems under some non-degeneracy conditions.
In this talk, analytic continuation of the Birkhoff normal forms is considered 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 continuation for the derivative of the inverse for the Birkhoff normal forms coincides with that of an elliptic fibration which naturally arises from the dynamics. Further, the global monodromy is concretely calculated as a representation of a colored braid group.
This talk is based on a joint work with Jean-Pierre Françoise (LJLL-UPMC).
Practical information
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- Free
Organizer
- Sonja Hohloch