Hausdorff Dimension of the Exceptional Set of Interval Piecewise Affine Contractions

• José Pedro Gaivão ^[1]
  1. [1] Universidade de Lisboa

     Universidade de Lisboa

     Socorro, Portugal

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 2, 2025
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • Let I = [0, 1), −1 <λ< 1 and f : I → I be a piecewise λ-affine map of the interval I. The exceptional set E f of f is the set of parameters δ ∈ R such that Rδ ◦ f is not asymptotically periodic, where Rδ : I → I is the rotation of angle δ. In this paper we prove that E f has zero Hausdorff dimension. We derive this result from a more general theorem concerning piecewise Lipschitz contractions on R that has independent interest.

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