STABILITY DOMAIN OF PLANAR SYMPLECTIC MAPS USING INVARIANT-MANIFOLDS

Authors
Citation
M. Giovannozzi, STABILITY DOMAIN OF PLANAR SYMPLECTIC MAPS USING INVARIANT-MANIFOLDS, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 53(6), 1996, pp. 6403-6412
Citations number
19
Categorie Soggetti
Physycs, Mathematical","Phsycs, Fluid & Plasmas
ISSN journal
1063651X
Volume
53
Issue
6
Year of publication
1996
Part
B
Pages
6403 - 6412
Database
ISI
SICI code
1063-651X(1996)53:6<6403:SDOPSM>2.0.ZU;2-0
Abstract
In a previous paper [Phys. Lett. A 182, 255 (1993)] we showed that, fo r the one-parameter area-preserving Henon map, the domain in phase spa ce where stable motion occurs can always be computed by using the inva riant manifolds emanating from the hyperbolic fixed point of period on e, regardless of the value of the parameter. We present here a general ization of this result to a large class of symplectic polynomial mappi ngs of the plane. Even in this case it is possible to show that the st ability domain is given by the inner envelope of the invariant manifol ds of a low period (one or two) hyperbolic fixed point. Numerical simu lations are presented. They were performed on different maps, includin g a model of relevance for accelerator physics.