Invariant curves of analytic perturbed nontwist area preserving maps

Carles Sim\'o, Departament de Matem\`atica Aplicada i An\`alisi, Universitat 
   de Barcelona, Gran Via 585, 08007 Barcelona (Spain)

Abstract

Area preserving maps close to integrable but not satisfying the twist
condition are studied. The existence of invariant curves is proved, but
they are no longer graphs with respect to the angular variable. Beyond
the generic, codimension 1 case, several higher codimension cases
are studied. Meandering curves, higher order meandering and labyrinthic
curves show up. Several examples illustrate that this behavior occurs in
very simple families of maps.
