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Stability of elliptic fixed points of analytic area-preserving mappings under the Bruno condition

Published online by Cambridge University Press:  30 September 2002

HELMUT RÜSSMANN
HELMUT RÜSSMANN
Affiliation:
Fachbereich Mathematik und Informatik, Universität Mainz, 55099 Mainz, Germany (e-mail: ruessmann@mathematik.uni-mainz.de)
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Abstract

We show the stability of an elliptic fixed point of an analytic area-preserving mapping under the Bruno condition, using Moser's Twist-mapping Theorem. We require that there are non-vanishing Birkhoff constants and prove the convergence of the transformation to the Birkhoff normal form if all Birkhoff constants are zero. The convergence theorem is formulated and proved for arbitrary dimensions.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 22 , Issue 5 , October 2002 , pp. 1551 - 1573
Copyright
© 2002 Cambridge University Press

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