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Random graph directed Markov systems
1. | Glendon College, York University, 2275 Bayview Avenue, Toronto |
2. | Department of Mathematics, University of North Texas, P.O. Box 311430, Denton, TX 76203-1430 |
References:
[1] |
A. Berlinkov and R. D. Mauldin, Packing measure and dimension of random fractals,, J. Theoret. Probab., 15 (2002), 695.
doi: 10.1023/A:1016271916074. |
[2] |
T. Bogenschuetz and V. M. Gundlach, Ruelle's transfer operator for random subshifts of finite type,, Ergod. Th. & Dynam. Sys., 15 (1995), 413.
|
[3] |
H. Crauel, "Random Probability Measures on Polish Spaces,", Stochastics Monographs, 11 (2002).
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[4] |
M. Denker, Y. Kifer and M. Stadlbauer, Thermodynamic formalism for random countable Markov shifts,, Discrete Contin. Dyn. Syst., 22 (2008), 131.
doi: 10.3934/dcds.2008.22.131. |
[5] |
S. Graf, Statistically self-similar fractals,, Probab. Theory Related Fields, 74 (1987), 357.
doi: 10.1007/BF00699096. |
[6] |
J. Kotus and M. Urbański, Hausdorff dimension and Hausdorff measures of Julia sets of elliptic functions,, Bull. London Math. Soc., 35 (2003), 269.
doi: 10.1112/S0024609302001686. |
[7] |
R. D. Mauldin and M. Urbański, Dimensions and measures in infinite iterated function systems,, Proc. London Math. Soc. (3), 73 (1996), 105.
doi: 10.1112/plms/s3-73.1.105. |
[8] |
R. D. Mauldin and M. Urbański, "Graph Directed Markov Systems: Geometry and Dynamics of Limit Sets,", Cambridge Tracts in Mathematics, 148 (2003).
|
[9] |
R. D. Mauldin and S. C. Williams, Random recursive constructions: Asymptotic geometric and topological properties,, Trans. Amer. Math. Soc., 295 (1986), 325.
doi: 10.1090/S0002-9947-1986-0831202-5. |
[10] |
V. Mayer, B. Skorulski and M. Urbański, Random distance expanding mappings, thermodynamic formalism, Gibbs measures, and fractal geometry,, preprint, (2008). Google Scholar |
[11] |
M. Stadlbauer, On random topological Markov chains with big images and preimages,, Stoch. Dyn., 10 (2010), 77.
doi: 10.1142/S0219493710002863. |
[12] |
B. Stratmann and M. Urbański, Pseudo-Markov systems and infinitely generated Schottky groups,, Amer. J. Math., 129 (2007), 1019.
doi: 10.1353/ajm.2007.0028. |
show all references
References:
[1] |
A. Berlinkov and R. D. Mauldin, Packing measure and dimension of random fractals,, J. Theoret. Probab., 15 (2002), 695.
doi: 10.1023/A:1016271916074. |
[2] |
T. Bogenschuetz and V. M. Gundlach, Ruelle's transfer operator for random subshifts of finite type,, Ergod. Th. & Dynam. Sys., 15 (1995), 413.
|
[3] |
H. Crauel, "Random Probability Measures on Polish Spaces,", Stochastics Monographs, 11 (2002).
|
[4] |
M. Denker, Y. Kifer and M. Stadlbauer, Thermodynamic formalism for random countable Markov shifts,, Discrete Contin. Dyn. Syst., 22 (2008), 131.
doi: 10.3934/dcds.2008.22.131. |
[5] |
S. Graf, Statistically self-similar fractals,, Probab. Theory Related Fields, 74 (1987), 357.
doi: 10.1007/BF00699096. |
[6] |
J. Kotus and M. Urbański, Hausdorff dimension and Hausdorff measures of Julia sets of elliptic functions,, Bull. London Math. Soc., 35 (2003), 269.
doi: 10.1112/S0024609302001686. |
[7] |
R. D. Mauldin and M. Urbański, Dimensions and measures in infinite iterated function systems,, Proc. London Math. Soc. (3), 73 (1996), 105.
doi: 10.1112/plms/s3-73.1.105. |
[8] |
R. D. Mauldin and M. Urbański, "Graph Directed Markov Systems: Geometry and Dynamics of Limit Sets,", Cambridge Tracts in Mathematics, 148 (2003).
|
[9] |
R. D. Mauldin and S. C. Williams, Random recursive constructions: Asymptotic geometric and topological properties,, Trans. Amer. Math. Soc., 295 (1986), 325.
doi: 10.1090/S0002-9947-1986-0831202-5. |
[10] |
V. Mayer, B. Skorulski and M. Urbański, Random distance expanding mappings, thermodynamic formalism, Gibbs measures, and fractal geometry,, preprint, (2008). Google Scholar |
[11] |
M. Stadlbauer, On random topological Markov chains with big images and preimages,, Stoch. Dyn., 10 (2010), 77.
doi: 10.1142/S0219493710002863. |
[12] |
B. Stratmann and M. Urbański, Pseudo-Markov systems and infinitely generated Schottky groups,, Amer. J. Math., 129 (2007), 1019.
doi: 10.1353/ajm.2007.0028. |
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