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 |
|---|---|
| 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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