2014/12/18 by Fuhrmann, Gabriel, Gröger, Maik, Jäger, Tobias
#37B55 #37C45 #37C70 #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.1412.6054
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.