Abstract:
A new possible geometry of an attractor of a dynamical system, a bony attractor, is described. A bony attractor is the union of two parts. The first part is the graph of a continuous function defined on a subset of $\Sigma^k$, the set of bi-infinite sequences of integers $m$ in the range $0\le m<k$. The second part is the union of uncountably many intervals contained in the closure of the graph. An open set of skew products over the Bernoulli shift $(\sigma\omega)_i=\omega_{i+1}$ with fiber $[0,1]$ is constructed such that each system in this set has a bony attractor.
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