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Convergent transformations into a normal form in analytic Hamiltonian systems with two degrees of freedom on the zero energy surface near degenerate elliptic singularities

Published online by Cambridge University Press:  18 October 2004

HELMUT RÜSSMANN
HELMUT RÜSSMANN
Affiliation:
Fachbereich Mathematik und Informatik, Universität Mainz, 55099 Mainz, Germany (e-mail: [email protected])
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Abstract

We study an analytic Hamiltonian system with two degrees of freedom, having the origin as an elliptic singularity. We assume that the full Birkhoff normal form exists and is divisible by its quadratic part, being indefinite. We show that under the Bruno condition and under the restriction to the zero energy surface, a real analytic transformation into a normal form exists. Such a normal form coincides with the restriction of the Birkhoff normal form to the zero energy surface up to an order as large as we want.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 24 , Issue 5 , October 2004 , pp. 1787 - 1832
Copyright
© 2004 Cambridge University Press

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