2026-04-13T03:05:09Zhttps://recercat.cat/oai/requestoai:recercat.cat:2445/1939182026-04-10T02:08:15Zcom_2072_1057col_2072_478917col_2072_478920
RECERCAT
author
Simó, Carles
author
Vieiro Yanes, Arturo
2023-02-21T18:36:42Z2023-02-21T18:36:42Z2009-04-162023-02-21T18:36:42Z
We consider a one-parameter family of area preserving maps in a neighbourhood of an elliptic fixed point. As the parameter evolves hyperbolic and elliptic periodic orbits of different periods are created. The exceptional resonances of order less than 5 have to be considered separately. The invariant manifolds of the hyperbolic periodic points bound islands containing the elliptic periodic points. Generically, these manifolds split. It turns out that the inner and outer splittings are different under suitable conditions. We provide accurate formulae describing the splittings of these manifolds as a function of the parameter and the relative values of these magnitudes as a function of geometric properties. The numerical agreement is illustrated using mainly the Hénon map as an example.
(c) IOP Publishing & London Mathematical Society , 2009 info:eu-repo/semantics/openAccess
Sistemes dinàmics de baixa dimensió
Teoria ergòdica
Homeomorfismes
Difeomorfismes
Low-dimensional dynamical systems
Ergodic theory
Homeomorphisms
Diffeomorphisms
Resonant zones, inner and outer splittings in generic and low order resonances of area preserving maps
info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion