Hausdorff measures versus equilibrium states of conformal infinite iterated function systems

Periodica Mathematica Hungarica

Volumn 37, Issue 1-3, 1998, Pages 153-205

  Urbański, Mariusz ^a,b  

^a University of North Texas ^*

^b UNIVERSITY OF NORTH TEXAS   (United States)

Author keywords

Almost periodic; Conformal and invariant measures; Density; Iterated function systems

Indexed keywords

EID: 54649084331     PISSN: 00315303     EISSN: 15882829     Source Type: Journal    
DOI: 10.1023/a:1004742822761     Document Type: Article

References (17)

1. [Bo] R. BOWEN, Equilibrium states and the ergodic theory for Anosov diffeomorphisms, Lecture Notes in Mathematics 470, Springer, 1975.
2. [DU1] M. DENKER and M. URBAŃSKI, The dichotomy of Hausdorff measures and equilibrium states for parabolic rational maps, in Proceedings of the conference on Ergodic Theory in Güstrow (1990), Lecture Notes in Mathematics 1514 (1992), 90-110.
3. [DU2] M. DENKER and M. URRAŃSKI, Relating Hausdorff measures and harmonic measures on parabolic, Jordan curves, Journal für die Reine and Angewandte Mathematik 450 (1994), 181-201.
4. [Fr] N. FRIEDMAN, Introduction to Ergodic Theory, New York, Cincinati, Toronto, London, Melbourne, Van Nostrand Reinhold Company, 1970.
5. [HU] P. HANUS and M. URBAŃSKI, Examples of positive recurrent functions, Preprint, 1998.
6. [HMU] P. HANUS, D. MAULDIN and M. URBAŃSKI, Multifractal analysis of conformal infinite iterated function systems, in preparation.
7. [IL] I. A. IBRAGIMOV and Y. V. LINNIK, Independent and stationary sequences of random variables, Wolters-Noordhoff Publ., Groningen, 1971.
8. [IM] C. IONESCH-TULCEA and G. MARINESCU, Théorie regodique pour des classes d'operations non-complement continues, Ann. Math. 52 (1950), 140-147.
9. [Ma] P. MATTILA, Geometry of Sets and Measures in Euclidean Spaces, Cambridge Studies in Advanced Mathematics 44, Cambridge University Press, 1995.
10. [MU1] D. MAULDIN and M. URBAŃSKI, Dimensions and measures in infinite iterated function systems, Proc. London Math. Soc. 73 (3) (1996), 105-154.
11. [MU2] D. MAULDIN and M. URBAŃSKI, Parabolic iterated function systems, Preprint, 1998.
12. [PS] W. PHILIPP and W. STOUT, Almost sure invariance principles for partial sums of weakly dependent random variables, Memoirs Amer. Math. Soc. 161 (2) (1975).
13. [PU] F. PRZYTYCKI and M. URBAŃSKI, Fractals in the Plane - Ergodic Theory Methods, to appear.
14. [PUZ.I] F. PRZYTYCKI, M. URBAŃSKI and A. ZDUNIK, Harmonic, Gibbs and Hausdorff measures on repellers for holomorphic maps I, Ann. of Math. 130 (1989), 1-40.
15. [PUZ,II] F. PRZYTYCKI, M. URBAŃSKI and A. ZDUNIK, Harmonic, Gibbs and Hausdorff measures on repellers for holomorphic maps II, Studia Math. 97 (1991), 189-225.
16. [Ry] M. RYCHLIK, Bounded variation and invariant measures, Studia Math. 76 (1983), 69-80.
17. [Sa] O. M. SARIG, Theormodynamic formalism For countable Markov shifts, to appear in Ergod. Th. and Dynam. Sys.