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This is the second part of the work devoted to the study of maps with decay in lattices. Here we apply the general theory developed in Fontich et al. (2011) to the study of hyperbolic sets. In particular, we establish that any close enough perturbation with decay of an uncoupled lattice map with a hyperbolic set has also a hyperbolic set, with dynamics on the hyperbolic set conjugated to the corresponding of the uncoupled map. We also describe how the decay properties of the maps are inherited by
the corresponding invariant manifolds.
CitationFontich, E.; De La Llave, R.; Martin, P. Dynamical systems on lattices with decaying interaction II: Hyperbolic sets and their invariant manifolds. "Journal of differential equations", 15 Març 2011, vol. 250, núm. 6, p. 2887-2926.
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