Abstract
We present a formula for the capacity of the graphs of certain fractal functions. We show that this formula can also be obtained using the Lyapunov exponents of an associated dynamical system.
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Moran, P.A.P.: Additive functions of intervals and Hausdorff measure. Proc. Camb. Phil. Soc.42, 15–23 (1946)
Hutchinson, J.: Fractals and self-similarity. Indiana Univ. Math. J.30, 5, 713–747 (1981)
Barnsley, M.F., Demko, S.: Iterated function systems and the global construction of fractals. Proc. R. Soc. Lond. A399, 243–275 (1985)
Barnsley, M.F., Harrington, A.N.: The calculus of fractal interpolation functions. Georgia Tech. preprint (1985)
Besicovitch, A.S., Ursell, H.D.: Sets of fractional dimensions, V: On dimensional numbers of some continuous curves. J. Lond. Math. Soc.12, 18–25 (1937)
Kaplan, J.L., Mallet-Paret, J., Yorke, J.A.: The Lyapunov dimension of a nowhere differentiable attracting torus. Ergodic Theory Dyn. Syst.4, 261–281 (1984)
Barnsley, M.F.: Fractal functions and interpolation. Georgia Tech. Preprint (1985)
Farmer, J.D., Ott, E., Yorke, J.A.: The dimension of chaotic attractors. Physica7D, 153–180 (1983)
Pelikan, S.: Invariant densities for random maps of the interval. Trans. Am. Math. Soc.281 (2), 313–325
Frederickson, P., Kaplan, J.L., Yorke, E.D., Yorke, J.A.: The Lyapunov dimension of strange attractors. J. Differ. Equations49, 185–207 (1983)
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Communicated by J.-P. Eckmann
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Hardin, D.P., Massopust, P.R. The capacity for a class of fractal functions. Commun.Math. Phys. 105, 455–460 (1986). https://doi.org/10.1007/BF01205937
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DOI: https://doi.org/10.1007/BF01205937