Geodesic
Bony Attractors
Funkcionalʹnyj analiz i ego priloženiâ, Tome 44 (2010) no. 3, pp. 73-76 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $0\le m$. 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.
Keywords: attractor, dynamical system, skew product, Bernoulli shift. 
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     author = {Yu. G. Kudryashov},
     title = {Bony {Attractors}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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     url = {http://geodesic.mathdoc.fr/item/FAA_2010_44_3_a7/}
}
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Yu. G. Kudryashov. Bony Attractors. Funkcionalʹnyj analiz i ego priloženiâ, Tome 44 (2010) no. 3, pp. 73-76. http://geodesic.mathdoc.fr/item/FAA_2010_44_3_a7/

[1] J. Milnor, Comm. Math. Phys., 99, 177–195 | DOI | MR | Zbl

[2] J. Hatchinson, Indiana Univ. Math. J., 30:5 (1981), 713–747 | DOI | MR