 07188 Henk Broer, Carles Simo, Renato Vitolo
 Hopfsaddlenode bifurcation for fixed points of 3Ddiffeomorphisms:
the Arnold resonance web
(15232K, PS)
Aug 2, 07

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Abstract. A model map Q for the Hopfsaddlenode (HSN) bifurcation of fixed
points of diffeomorphisms is studied. The model is constructed to
describe the dynamics inside an attracting invariant twotorus which
occurs due to the presence of quasiperiodic Hopf bifurcations of an
invariant circle, emanating from the central HSN
bifurcation. Resonances of the dynamics inside the twotorus attractor
yield an intricate structure of gaps in parameter space, the socalled
Arnol d resonance web. Particularly interesting dynamics occurs near
the multiple crossings of resonance gaps, where a web of hyperbolic
periodic points is expected to occur inside the twotorus
attractor. It is conjectured that heteroclinic intersections of the
invariant manifolds of the saddle periodic points may give rise to the
occurrence of strange attractors contained in the twotorus. This is a
concrete route to the NewhouseRuelleTakens scenario. To understand
this phenomenon, a simple model map of the standard twotorus is
developed and studied and the relations with the starting model map Q
are discussed.
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