Iterated function system and Ruelle operator

Journal of Mathematical Analysis and Applications

Volumn 231, Issue 2, 1999, Pages 319-344

  Fan, Ai Hua ^a   Lau, Ka Sing ^b  

^a UNIVERSITÉ DE CERGY PONTOISE   (France)

^b UNIVERSITY OF PITTSBURGH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000079707     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1998.6210     Document Type: Article

References (26)

1. Barnsley M. F., Demko S. G., Elton J. H., Geromino J. S. Invariant measures for Markov processes arising from iterated function systems with place-dependent probabilities. Ann. Inst. H. Poincaré 24:1988;367-394.
2. Bohr T., Rand D. The entropy function for characteristic exponents. Phys. D. 25:1987;387-398.
3. Bowen R. Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms. Lecture Notes in Math. 470:1975;Springer-Verlag, Berlin.
4. Cawley R., Mauldin R. D. Multifractal decompositions of Moran fractals. Adv. in Math. 92:1992;196-236.
5. Dunford N., Schwartz J. T. Linear Operator, Part I. 1958;Wiley-Interscience, New York.
6. Falconer K. J. Fractal Geometry. 1990;Wiley, New York.
7. Fan A. H. Sur les dimensions de mesures. Studia Math. 111:1994;1-17.
8. Fan A. H. A proof of the Ruelle theorem. Rev. Math. Phys. 7:1995;1241-1247.
9. Fan A. H. Ergodicity, unidimensionality and multifractality of self-similar measures. Kyushu J. Math. 50:1996;541-574.
10. Hata M. On some properties of set dynamical systems. Proc. Japan Acad. Ser. A Math. Sci. 61:1985;99-102.
11. Hennion L. Sur un théorème spectral et ses applications aux noyaux lipschitziens. Proc. Amer. Math. Soc. 118:1993;627-634.
12. Hutchinson J. E. Fractals and self-similarity. Indian Univ. Math. J. 30:1981;713-747.
13. Lau K. S., Wang J. R. Mean quadratic variations and Fourier asymptotics of self-similar measures. Monatsh. Math. 115:1993;99-132.
14. Lau K. S., Ngai S. M. Multifractal measures and a weak separation property. Adv. in Math. 141:1999;45-96.
15. q-spectrum of a measure. Proc. Amer. Math. Soc. 125:1997;2943-2951.
16. Mauldin D., Urbański M. Dimension and measures in infinite function systems. Proc. London Math. Soc. 73:1996;105-154.
17. A. Öberg, Approximation of invariant measures for random iterations.
18. Patzschke N. Self-conformal multifractals. Adv. Appl. Math. 19:1997;486-513.
19. Pesin M., Weiss H. A multifractal analysis of equilibrium measures for conformal expanding maps and Moran-like geometric contractions. J. Statist. Phys. 86:1997;233-275.
20. 1g. Ergodic Theory Dynamical Systems. 16:1996;531-543.
21. Rand D. The singularity spectrumf. Ergodic Theory Dynamical Systems. 9:1989;527-541.
22. Rudin W. Real and Complex Analysis. 1987;McGraw-Hill, New York.
23. Ruelle D. Thermodynamic Formalism: The Mathematical Structures of Classical Equilibrium Statistical Mechanics. Encyclopedia Math. Appl. 5:1978;Addison-Wesley, Reading.
24. Schief A. Separation properties of self-similar sets. Proc. Amer. Math. Soc. 112:1994;111-115.
25. Strichartz R. Self-similar measures and their Fourier transform, III. Indiana Univ. Math. J. 42:1993;367-411.
26. Strichartz R., Taylor A., Zhang T. Densities of self-similar measures on the line. Experimental Math. 4:1995;101-128.