The Newhouse set has a positive Hausdorff dimension

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Abstract

The Newhouse phenomenon of infinitely many coexisting periodic attractors is studied in its simplest form. One shows that the corresponding parameter set (the Newhouse set)JN has a strictly positive Hausdorff dimension. This result is stronger than that of Tedeschini-Lalli and Yorke [Commun. Math. Phys. 106, 635 (1986)] concerning the Lebesgue measure of the Newhouse set; and is complementary to our knowledge on the topological properties of JN, namely it is a residual set, hence uncountable and everywhere dense in a parameter interval.

Original languageEnglish (US)
Pages (from-to)317-332
Number of pages16
JournalCommunications In Mathematical Physics
Volume131
Issue number2
DOIs
StatePublished - Jul 1990

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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