## 2006.95: Milnor attractors and topological attractors of a piecewise linear map

2006.95:
Paul Glendinning
(2001)
*Milnor attractors and topological attractors of a piecewise linear map.*
Nonlinearity, 14 (2).
pp. 239-258.
ISSN 0951-7715

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DOI: 10.1088/0951-7715/14/2/304

## Abstract

A very simple two-dimensional map is discussed. It is shown that for appropriate values of the parameters there is a two dimensional subset of the plane on which the dynamics is transitive and periodic orbits are dense, but that this topological attractor contains a one dimensional set which attracts almost all points (i.e. it is a Milnor attractor). This arises naturally as a precursor to a blowout bifurcation to on-off intermittency in this system, and confirms a conjecture due to Pikovsky and Grassberger.

Item Type: | Article |
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Additional Information: | Note that in the published version an unfortunate minus sign creeps into the second line of equation (1.2). The original version on this eprint is correct. |

Subjects: | MSC 2000 > 37 Dynamical systems and ergodic theory |

MIMS number: | 2006.95 |

Deposited By: | Professor Paul Glendinning |

Deposited On: | 17 May 2006 |

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