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Title: Stability of degenerated fixed points of analytic area preserving mappings
Author: Simó, Carles
Keywords: Dinàmica topològica
Varietats (Matemàtica)
Universitat de Barcelona. Institut de Matemàtica
Issue Date: 1982
Publisher: Universitat de Barcelona
Series/Report no: Mathematics Preprint Series; 3
Abstract: It js well known that hyperbolic points of an analytic area preserving mapping (APM) T are unstable. As a Corollary of Moser's twist thcorem the elliptic ones are stable provided the eigenvalues l. of DT at the fixed point are nota k-th root of t.he unity, k~ lf2p+2 p ~l. and any of the first p coefficients of the Birkhoff normal form is non-zero. To end the study of the stability of fixed μoints we study the parabolic ar degenerated case. Elliptic points far which stability can not be decided using directly Moser' s theorem (specially if " is a third or fourth root of the uni ty) can be reduced to the parabolic case taking a suitable power of T. The main result is that a degenerated fixed point of an analytic APM is stable if and only if the generating function of T, with the part which generates the identity suppressed, has a strict extremum at the fixed point. Sorne examples and comment are included.
Note: Preprint enviat per a la seva publicació en una revista científica: Astérisque, 1982, num. 98-99, p. 184-194
Note: Reproducció digital del document original en paper [CRAI Biblioteca de Matemàtiques i Informàtica - Dipòsit Departament CAIXA 31.3]
Appears in Collections:Preprints de Matemàtiques - Mathematics Preprint Series

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