The Newhouse set has a positive Hausdorff dimension
type: Item
instance of: scholarly article
title: The Newhouse set has a positive Hausdorff dimension
zbMATH Open document ID: 0708.58017
DOI: 10.1007/BF02161417
author: Xiaojing Wang
published in: Communications in Mathematical Physics
publication date: 1990-01-01T00:00:00Z
review text: As observed first by \textit{S. E. Newhouse} [Topology 13, 9-18 (1974; Zbl 0275.58016), Publ. Math., Inst. Hautes Etud. Sci. 50, 101-152 (1979; Zbl 0445.58022)] an infinite number of periodic attractors may coexist in a bounded region of a multidimensional dynamical system. The author constructs a one-parameter family of planar diffeomorphisms which shows this phenomenon for a set of parameters with positive Hausdorff dimension.
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 37C25
zbMATH DE Number: 4163773
zbMATH Keywords: Newhouse phenomenon
zbMATH Keywords: periodic attractors
zbMATH Keywords: planar diffeomorphisms
zbMATH Keywords: Hausdorff dimension
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02161417
OpenAlex ID: W1966005951
description: scientific article; zbMATH DE number 4163773