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 ∑k, the set of bi-infinite sequences of integers m in the range 0 ≤ 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 (σω) i = ωi+1 with fiber [0,1] is constructed such that each system in this set has a bony attractor.
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References
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Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 44, No. 3, pp. 73–76, 2010
Original Russian Text Copyright © by Yu. G. Kudryashov
The work is supported by RFBR grants nos. 07-01-00017-a and 10-01-00739-a and by RFBR-CNRS grant no. 05-01-02801-CNRS_a
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Kudryashov, Y.G. Bony attractors. Funct Anal Its Appl 44, 219–222 (2010). https://doi.org/10.1007/s10688-010-0028-8
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DOI: https://doi.org/10.1007/s10688-010-0028-8