A dimension result arising from the L'-spectrum of a measure

Proceedings of the American Mathematical Society

Volumn 125, Issue 10, 1997, Pages 2943-2951

  Ngai, Sze Man ^a  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Entropy dimension; Hausdorff dimension; Lq spectrum

Indexed keywords

EID: 21944433331     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9939-97-03974-9     Document Type: Article

References (21)

1. [AP] M. Arbeiter and N. Patzschke, Random self-similar multifractals, Math. Nachr. 181 (1996), 5-42. CMP 97:01
2. [AY] J.C. Alexander and J.A. Yorke, Fat baker's transformations, Ergodic Theory Dynamical Systems. 4 (1984), 1-23. MR 86c:58090
3. [AZ] J.C. Alexander and D. Zagier, The entropy of a certain infinitely convolved Bernoulli measure, J. London Math. Soc. 44 (1991), 121-134. MR 92g:28035
4. R. Cawley and R.D. Mauldin, Multifractal decompositions of Moran fractals, Adv. Math. 92 (1992), 196-236. MR 93b:58085
5. [E] P. Erdös, On a family of symmetric Bernoulli convolutions, Amer. J. Math. 61 (1939), 974-976. MR l:52a
6. [F] K.J. Falconer, Fractal geometry-Mathematical foundations and applications, John Wiley and Sons, New York, 1990. MR 92j:28008
7. [Fa] A.-H. Fan, Multifractal analysis of infinite products, J. Statist. Phys. 86 (1997), 1313-1336.
8. [GH] J.S. Geronimo and D.P. Hardin, An exact formula for the measure dimensions associated with a class of piecewise linear maps, Constr. Approx. 5 (1989), 89-98. MR 90d:58076
9. [H] T.C. Halsey, M. H. Jensen, L.P. Kadanoff, I. Procaccia and B.I. Shraiman, fractal measures and their singularities: The characterization of strange sets, Phys. Rev. A 33 (1986), 1141-1151. MR87h:58125a
10. [HP] H. Hentschel and I. Procaccia, The infinite number of generalized dimensions of fractals and strange attractors, Physica 8D (1983), 435-444. MR 85a:58064
11. [Hut] J.E. Hutchinson, Fractals and self similarity, Indiana Univ. Math. J. 30 (1981), 713-747. MR 82h:49026
12. [La] S.P. Lalley, Random series in powers of algebraic integers: Hausdorff dimension of the limit distribution, preprint.
13. [LN1] K.-S. Lau and S.-M. Ngai, Multifractal measures and a weak separation condition, Adv. Math, (to appear).
14. q-spectrum of the Bernoulli convolution associated with the golden ratio, preprint.
15. [LP] F. Ledrappier and A. Porzio, A dimension formula for Bernoulli convolutions, J. Statist. Phys. 76 (1994), 1307-1327. MR 95i:58111
16. [PW] Y. Pesin and H. Weiss, A multifractal analysis of equilibrium measures for conformai expanding maps and Moran-like geometric constructions, J. Statist. Phys. 86 (1997), 233-275.
17. [R] D.A. Rand, The singularity spectrum f(a) for cookie-cutters, Ergodic Theory Dynamical Systems. 9 (1989), 527-541. MR 90k:58115
18. [Re] A. Rényi, Probability Theory, North-Holland, Amsterdam, 1970. MR 47:4296
19. [Ro] R.T. Rockafellar, Convex analysis, Princeton University Press, Princeton, New Jersey, 1970. MR 43:445
20. [S] R.S. Strichartz, Self-similar measures and their Fourier transforms I, Indiana Univ. Math. J. 39 (1990), 797-817. MR 92k:42015
21. [Y] L.-S. Young, Dimension, entropy and Lyapunov exponents, Ergodic Theory Dynamical Systems. 2 (1982), 109-124. MR 84h:58087