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.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics