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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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.
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|
|Deposited By:||Professor Paul Glendinning|
|Deposited On:||17 May 2006|