A spectral decomposition for singular-hyperbolic sets

• Autores: Carlos Morales, María José Pacífico
• Localización: Pacific journal of mathematics, ISSN 0030-8730, Vol. 229, Nº 1, 2007, págs. 223-232
• Idioma: inglés
• DOI: 10.2140/pjm.2007.229.223
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• Resumen

  • We extend the Spectral Decomposition Theorem for hyperbolic sets to singular-hyperbolic sets on 3-manifolds. We prove that an attracting singular-hyperbolic set with dense periodic orbits and a unique equilibrium of a Cr vector field, where r = 1, is a finite union of transitive sets; the union is disjoint or the set contains finitely many distinct homoclinic classes. If the vector field is Cr-generic, the union is in fact disjoint.