The Newhouse set has a positive Hausdorff dimension

Xiao Jing Wang

doi:10.1007/BF02161417

The Newhouse set has a positive Hausdorff dimension

Xiao Jing Wang

Neural Science

Research output: Contribution to journal › Article › peer-review

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)J_N 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 J_N, namely it is a residual set, hence uncountable and everywhere dense in a parameter interval.

Original language	English (US)
Pages (from-to)	317-332
Number of pages	16
Journal	Communications In Mathematical Physics
Volume	131
Issue number	2
DOIs	https://doi.org/10.1007/BF02161417
State	Published - Jul 1990

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF02161417

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The Newhouse set has a positive Hausdorff dimension

Abstract

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