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Stability of degenerated fixed points of analytic area preserving mappings
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Resum
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.
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Preprint enviat per a la seva publicació en una revista científica: Astérisque, 1982, num. 98-99, p. 184-194
Matèries (anglès)
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Citació
SIMÓ, Carles. Stability of degenerated fixed points of analytic area preserving mappings. [consulted: 19 of August of 2026]. Available at: https://hdl.handle.net/2445/151240