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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


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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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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