Non-smooth saddle-node bifurcations II: dimensions of strange attractors
Dynamical Systems
2014-12-22 v2
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.
Keywords
Cite
@article{arxiv.1412.6054,
title = {Non-smooth saddle-node bifurcations II: dimensions of strange attractors},
author = {Gabriel Fuhrmann and Maik Gröger and Tobias Jäger},
journal= {arXiv preprint arXiv:1412.6054},
year = {2014}
}