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Bedford, Tim

On Weierstrass-like functions and random recurrent sets. (English) Zbl 0732.26009

Math. Proc. Camb. Philos. Soc. 106, No. 2, 325-342 (1989).
Summary: A construction of Weierstrass-like functions using recurrent sets is described, and the Hausdorff dimensions of the graphs are computed. An important part of the proof is the notion of a globally random recurrent set. The Hausdorff dimension of a class of such sets is calculated using techniques of random matrix products.

Cited in 15 Documents

MSC:

26A27 Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives
28A78 Hausdorff and packing measures
28A80 Fractals

Keywords:

Weierstrass-like functions; Hausdorff dimensions; graphs; random recurrent set; random matrix products
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References:

[1] DOI: 10.1112/jlms/s1-12.45.18 · Zbl 0016.01703 · doi:10.1112/jlms/s1-12.45.18
[2] Bougerol, Products of Random Matrices with Application to Schrödinger Operators (1985) · Zbl 0572.60001 · doi:10.1007/978-1-4684-9172-2
[3] Billingsley, Ergodic Theory of Information (1965) · Zbl 0141.16702
[4] DOI: 10.1090/S0002-9947-1986-0860394-7 · doi:10.1090/S0002-9947-1986-0860394-7
[5] DOI: 10.1090/S0002-9947-1986-0831202-5 · doi:10.1090/S0002-9947-1986-0831202-5
[6] DOI: 10.1016/0001-8708(82)90066-4 · Zbl 0495.51017 · doi:10.1016/0001-8708(82)90066-4
[7] McMullen, Nagoya Math. J. 96 pp 1– (1984) · Zbl 0539.28003 · doi:10.1017/S0027763000021085
[8] DOI: 10.1007/BF03167911 · Zbl 0685.26008 · doi:10.1007/BF03167911
[9] DOI: 10.1017/S0305004100066299 · Zbl 0623.60020 · doi:10.1017/S0305004100066299
[10] DOI: 10.1093/qmath/os-20.1.31 · Zbl 0031.20801 · doi:10.1093/qmath/os-20.1.31
[11] DOI: 10.1017/S0305004100029236 · doi:10.1017/S0305004100029236
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