 99480 Emilia Petrisor
 Nontwist area preserving maps with reversing symmetry group
(66K, LATeX 2e)
Dec 16, 99

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Abstract. The aim of this paper is to give a theoretical explanation of the
rich phenomenology exhibited by nontwist mappings of the cylinder,
in numerical experiments reported in {[delCastillo {\it et al},
1996]}, {[Howard \& Humpherys, 1995]},
and to give new insights in the dynamics of nontwist
standardlike maps. Our approach is based on the reversing
symmetric properties of the nontwist standardlike systems. We
relate the bifurcation of periodic orbits of such maps to their
position with respect to a groupinvariant circle, and to a
critical circle, at whose points the twist property is violated.
Moreover, we show that appearance of the meanders, i.e.
homotopically nontrivial invariant circles of the cylinder,
that are not graphs of real functions of angular variable,
is a global bifurcation of a curve on the cylinder,
with nodaltype singularities, and invariant with respect to the
action of a reversing symmetry group.
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