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arXiv · 1412.6054

Non-smooth saddle-node bifurcations II: dimensions of strange attractors

Gabriel Fuhrmann·Maik Gröger·Tobias Jäger
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Abstract

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 to describe the topological structure of the attractors and to prove their minimality.

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Gabriel Fuhrmann, Maik Gröger, Tobias Jäger. 2014-12-19. Non-smooth saddle-node bifurcations II: dimensions of strange attractors. https://arxiv.org/abs/1412.6054

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