Whitney regularity for solutions to the coboundary equation on Cantor sets

• Autores: Matthew Nicol, Andrei Török
• Localización: Mathematical Physics Electronic Journal, ISSN-e 1086-6655, Vol. 13, Nº 6, 2007
• Idioma: inglés
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• Resumen

  • We prove Whitney regularity results for the solutions of the coboundary equation over dynamically defined Cantor sets satisfying a natural geometric regularity condition, in particular hyperbolic basic sets in dimension two. To do this we prove an analogue of Journe's well-known result in the context of Cantor sets satisfying geometric regularity conditions.