Non-smooth saddle-node bifurcations II: Dimensions of strange attractors
Copyright policy )Non-smooth saddle-node bifurcations II: Dimensions of strange attractors
We study the geometric and topological properties of strange non-chaotic attractors created in non-smooth saddle-node bifurcations of quasiperiodically forced interval maps. By interpreting the attractors as limit objects of the iterates of a continuous curve and controlling the geometry of the latter, we determine their Hausdorff and box-counting dimension and show that these take distinct values. Moreover, the same approach allows us to describe the topological structure of the attractors and to prove their minimality.
- Jagiellonian University Poland
- University of Bremen Germany
- TU Dresden Germany
ddc:510, 37B55, 37C45, 37C70, Dynamical aspects of attractors and their bifurcations, Dynamical Systems (math.DS), strange non-chaotic attractors, Strange attractors, chaotic dynamics of systems with hyperbolic behavior, Dynamical systems involving maps of the interval, Hausdorff and box-counting dimension, Hausdorff and packing measures, nicht-chaotische Attraktoren, nicht glatte Sattel-Knoten-Bifurkationen, Hausdorff- und Kastenzähldimension, non-chaotic attractors,non-smooth saddle-node bifurcations, Hausdorff and box-counting dimension, FOS: Mathematics, monotone interval maps, Mathematics - Dynamical Systems, non-smooth bifurcations, info:eu-repo/classification/ddc/510
ddc:510, 37B55, 37C45, 37C70, Dynamical aspects of attractors and their bifurcations, Dynamical Systems (math.DS), strange non-chaotic attractors, Strange attractors, chaotic dynamics of systems with hyperbolic behavior, Dynamical systems involving maps of the interval, Hausdorff and box-counting dimension, Hausdorff and packing measures, nicht-chaotische Attraktoren, nicht glatte Sattel-Knoten-Bifurkationen, Hausdorff- und Kastenzähldimension, non-chaotic attractors,non-smooth saddle-node bifurcations, Hausdorff and box-counting dimension, FOS: Mathematics, monotone interval maps, Mathematics - Dynamical Systems, non-smooth bifurcations, info:eu-repo/classification/ddc/510
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