### 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) |
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Pages (from-to) | 317-332 |

Number of pages | 16 |

Journal | Communications in Mathematical Physics |

Volume | 131 |

Issue number | 2 |

DOIs | |

State | Published - Jul 1990 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics

### Cite this

**The Newhouse set has a positive Hausdorff dimension.** / Wang, Xiao-Jing.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 131, no. 2, pp. 317-332. https://doi.org/10.1007/BF02161417

}

TY - JOUR

T1 - The Newhouse set has a positive Hausdorff dimension

AU - Wang, Xiao-Jing

PY - 1990/7

Y1 - 1990/7

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0038949437&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0038949437&partnerID=8YFLogxK

U2 - 10.1007/BF02161417

DO - 10.1007/BF02161417

M3 - Article

VL - 131

SP - 317

EP - 332

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 2

ER -