-
Previous Article
Non-integrability of the collinear three-body problem
- DCDS Home
- This Issue
-
Next Article
On the ill-posedness result for the BBM equation
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), 695-713.
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), 413-447. |
[3] |
H. Crauel, "Random Probability Measures on Polish Spaces," Stochastics Monographs, 11, Taylor and Francis, 2002. |
[4] |
M. Denker, Y. Kifer and M. Stadlbauer, Thermodynamic formalism for random countable Markov shifts, Discrete Contin. Dyn. Syst., 22 (2008), 131-164.
doi: 10.3934/dcds.2008.22.131. |
[5] |
S. Graf, Statistically self-similar fractals, Probab. Theory Related Fields, 74 (1987), 357-392.
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), 269-275.
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), 105-154.
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, Cambridge, 2003. |
[9] |
R. D. Mauldin and S. C. Williams, Random recursive constructions: Asymptotic geometric and topological properties, Trans. Amer. Math. Soc., 295 (1986), 325-346.
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, can be found at www.math.unt.edu/ urbanski. |
[11] |
M. Stadlbauer, On random topological Markov chains with big images and preimages, Stoch. Dyn., 10 (2010), 77-95.
doi: 10.1142/S0219493710002863. |
[12] |
B. Stratmann and M. Urbański, Pseudo-Markov systems and infinitely generated Schottky groups, Amer. J. Math., 129 (2007), 1019-1062.
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), 695-713.
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), 413-447. |
[3] |
H. Crauel, "Random Probability Measures on Polish Spaces," Stochastics Monographs, 11, Taylor and Francis, 2002. |
[4] |
M. Denker, Y. Kifer and M. Stadlbauer, Thermodynamic formalism for random countable Markov shifts, Discrete Contin. Dyn. Syst., 22 (2008), 131-164.
doi: 10.3934/dcds.2008.22.131. |
[5] |
S. Graf, Statistically self-similar fractals, Probab. Theory Related Fields, 74 (1987), 357-392.
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), 269-275.
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), 105-154.
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, Cambridge, 2003. |
[9] |
R. D. Mauldin and S. C. Williams, Random recursive constructions: Asymptotic geometric and topological properties, Trans. Amer. Math. Soc., 295 (1986), 325-346.
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, can be found at www.math.unt.edu/ urbanski. |
[11] |
M. Stadlbauer, On random topological Markov chains with big images and preimages, Stoch. Dyn., 10 (2010), 77-95.
doi: 10.1142/S0219493710002863. |
[12] |
B. Stratmann and M. Urbański, Pseudo-Markov systems and infinitely generated Schottky groups, Amer. J. Math., 129 (2007), 1019-1062.
doi: 10.1353/ajm.2007.0028. |
[1] |
Manfred Denker, Yuri Kifer, Manuel Stadlbauer. Thermodynamic formalism for random countable Markov shifts. Discrete and Continuous Dynamical Systems, 2008, 22 (1&2) : 131-164. doi: 10.3934/dcds.2008.22.131 |
[2] |
Manfred Denker, Yuri Kifer, Manuel Stadlbauer. Corrigendum to: Thermodynamic formalism for random countable Markov shifts. Discrete and Continuous Dynamical Systems, 2015, 35 (1) : 593-594. doi: 10.3934/dcds.2015.35.593 |
[3] |
Thomas Jordan, Mark Pollicott. The Hausdorff dimension of measures for iterated function systems which contract on average. Discrete and Continuous Dynamical Systems, 2008, 22 (1&2) : 235-246. doi: 10.3934/dcds.2008.22.235 |
[4] |
Kanji Inui, Hikaru Okada, Hiroki Sumi. The Hausdorff dimension function of the family of conformal iterated function systems of generalized complex continued fractions. Discrete and Continuous Dynamical Systems, 2020, 40 (2) : 753-766. doi: 10.3934/dcds.2020060 |
[5] |
Markus Böhm, Björn Schmalfuss. Bounds on the Hausdorff dimension of random attractors for infinite-dimensional random dynamical systems on fractals. Discrete and Continuous Dynamical Systems - B, 2019, 24 (7) : 3115-3138. doi: 10.3934/dcdsb.2018303 |
[6] |
Michael Jakobson, Lucia D. Simonelli. Countable Markov partitions suitable for thermodynamic formalism. Journal of Modern Dynamics, 2018, 13: 199-219. doi: 10.3934/jmd.2018018 |
[7] |
Yakov Pesin. On the work of Sarig on countable Markov chains and thermodynamic formalism. Journal of Modern Dynamics, 2014, 8 (1) : 1-14. doi: 10.3934/jmd.2014.8.1 |
[8] |
Welington Cordeiro, Manfred Denker, Michiko Yuri. A note on specification for iterated function systems. Discrete and Continuous Dynamical Systems - B, 2015, 20 (10) : 3475-3485. doi: 10.3934/dcdsb.2015.20.3475 |
[9] |
David Cheban, Cristiana Mammana. Continuous dependence of attractors on parameters of non-autonomous dynamical systems and infinite iterated function systems. Discrete and Continuous Dynamical Systems, 2007, 18 (2&3) : 499-515. doi: 10.3934/dcds.2007.18.499 |
[10] |
Davide La Torre, Simone Marsiglio, Franklin Mendivil, Fabio Privileggi. Public debt dynamics under ambiguity by means of iterated function systems on density functions. Discrete and Continuous Dynamical Systems - B, 2021, 26 (11) : 5873-5903. doi: 10.3934/dcdsb.2021070 |
[11] |
Saisai Shi, Bo Tan, Qinglong Zhou. Best approximation of orbits in iterated function systems. Discrete and Continuous Dynamical Systems, 2021, 41 (9) : 4085-4104. doi: 10.3934/dcds.2021029 |
[12] |
Tomasz Szarek, Mariusz Urbański, Anna Zdunik. Continuity of Hausdorff measure for conformal dynamical systems. Discrete and Continuous Dynamical Systems, 2013, 33 (10) : 4647-4692. doi: 10.3934/dcds.2013.33.4647 |
[13] |
Nhan-Phu Chung. Gromov-Hausdorff distances for dynamical systems. Discrete and Continuous Dynamical Systems, 2020, 40 (11) : 6179-6200. doi: 10.3934/dcds.2020275 |
[14] |
Lianfa He, Hongwen Zheng, Yujun Zhu. Shadowing in random dynamical systems. Discrete and Continuous Dynamical Systems, 2005, 12 (2) : 355-362. doi: 10.3934/dcds.2005.12.355 |
[15] |
Philippe Marie, Jérôme Rousseau. Recurrence for random dynamical systems. Discrete and Continuous Dynamical Systems, 2011, 30 (1) : 1-16. doi: 10.3934/dcds.2011.30.1 |
[16] |
Pablo G. Barrientos, Abbas Fakhari, Aliasghar Sarizadeh. Density of fiberwise orbits in minimal iterated function systems on the circle. Discrete and Continuous Dynamical Systems, 2014, 34 (9) : 3341-3352. doi: 10.3934/dcds.2014.34.3341 |
[17] |
Vaughn Climenhaga. Multifractal formalism derived from thermodynamics for general dynamical systems. Electronic Research Announcements, 2010, 17: 1-11. doi: 10.3934/era.2010.17.1 |
[18] |
Yujun Zhu. Preimage entropy for random dynamical systems. Discrete and Continuous Dynamical Systems, 2007, 18 (4) : 829-851. doi: 10.3934/dcds.2007.18.829 |
[19] |
Ji Li, Kening Lu, Peter W. Bates. Invariant foliations for random dynamical systems. Discrete and Continuous Dynamical Systems, 2014, 34 (9) : 3639-3666. doi: 10.3934/dcds.2014.34.3639 |
[20] |
Weigu Li, Kening Lu. Takens theorem for random dynamical systems. Discrete and Continuous Dynamical Systems - B, 2016, 21 (9) : 3191-3207. doi: 10.3934/dcdsb.2016093 |
2020 Impact Factor: 1.392
Tools
Metrics
Other articles
by authors
[Back to Top]