Vector-valued multifractal measures

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 452, Issue 1949, 1996, Pages 1433-1457

  Falconer, Kenneth J ^a   O'Neil, Toby C ^a  

^a UNIVERSITY OF ST ANDREWS   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33744982308     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.1996.0073     Document Type: Article

References (22)

1. Arbeiter, M. & Patzscke, N. 1996 Random self-similar multifractals. Preprint.
2. Bessis, D., Paladin, G., Turchetti, G. &: Vaienti, S. 1988 Generalized dimensions, entropies, and Liapunov exponents from the pressure function for strange sets. J. Statist. Phys. 51, 109-134.
3. Cawley, R. & Mauldin, R. D. 1992 Multifractal decomposition of Moran fractals. Adv. Math 92, 196-236.
4. Dunford, N. & Schwartz, J. T. 1963 Linear operators, vol. I. Wiley.
5. Edwards, R. E. 1965 Functional analysis -theory and applications. Holt, Rinehart and Winston.
6. Edgar, G. A. &: Mauldin, R. D. 1992 Multifractal decomposition of digraph recursive fractals. Proc. Land. Math. Soc. 65(3), 604-628.
7. Evertz, C. J. G. & Mandelbrot, B. B. 1992 Multifractal measures (Appendix B). In Chaos and fractals: new frontiers of science (ed. H.-O. Peitgen, H. Jürgens & D. Saupe). Springer.
8. Falconer, K. J. 1990 Fractal geometry: mathematical foundations and applications. Wiley.
9. Falconer, K. J. 1994 The multifractal spectrum of statistically self-similar meaures. J. Theor. Prob. 7, 681-702.
10. Halsey, T. C., Jensen, M. H., Kadanoff, L. P., Procaccia, I. & Shraiman, B. J. 1986 Fractal measures and their singularities: the characterization of strange sets. Phys. Rev. A 33, 1141-1151.
11. Hutchinson, J. E. 1981 Fractals and self similarity. Indiana Univ. Math. Jl 30, 713-747.
12. Lalley, S. P. 1988 The packing and covering functions of some self-similar fractals. Indiana Univ. Math. Jl 37, 699-710.
13. Lalley, S. P. 1989 Renewal theorems in symbolic dynamics, with applications to geodesic flow, non-euclidean tesselations and their fractal limits. Ada Math. 163, 1-55.
14. Lalley, S. P. 1991 Probabilistic methods in certain counting problems of ergodic theory. In Ergodic theory, symbolic dynamics and hyperbolic spaces, pp. 223-258. Oxford University Press.
15. Lau, K. & Ngai, S. 1996 Multifractal measures and a weak separation condition. Preprint.
16. Mandelbrot, B. B. 1974 Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier. J. Fluid Mech. 62, 331-358.
17. Mandelbrot, B. B. 1982 The fractal geometry of nature. W. H. Freeman.
18. Mattila, P. 1995 The geometry of sets and measures in Euclidean spaces. Cambridge University Press.
19. Olsen, L. 1994 Random geometrically graph directed self-similar multifractals. Pitman.
20. Olsen, L. 1996 A multifractal formalism. Adv. Math. 116, 82-196.
21. Strichartz, R. S. 1993a Self-similar measures and their Fourier transforms. II. Trans. Am. Math. Soc. 336, 335-361.
22. Strichartz, R. S. 19936 Self-similar measures and their Fourier transforms. III. Indiana Univ. Math. J/42, 367-411.