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Fixed points of elliptic reversible transformations with integrals

Published online by Cambridge University Press:  19 September 2008

Xianghong Gong
Xianghong Gong
Affiliation:
Department of Mathematics, University of Chicago, Chicago, IL 60637, USA
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Abstract

We show that for a certain family of integrable reversible transformations, the curves of periodic points of a general transformation cross the level curves of its integrals. This leads to the divergence of the normal form for a general reversible transformation with integrals. We also study the integrable holomorphic reversible transformations coming from real analytic surfaces in ℂ2 with non-degenerate complex tangents. We show the existence of real analytic surfaces with hyperbolic complex tangents, which are contained in a real hyperplane, but cannot be transformed into the Moser—Webster normal form through any holomorphic transformation.

Type
Survey Article
Information
Ergodic Theory and Dynamical Systems , Volume 16 , Issue 4 , August 1996 , pp. 683 - 702
Copyright
Copyright © Cambridge University Press 1996

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