
Previous Article
On dimensions of conformal repellers. Randomness and parameter dependency
 DCDS Home
 This Issue

Next Article
The Ruelle spectrum of generic transfer operators
A new variation of Bowen's formula for graph directed Markov systems
1.  Glendon College, York University, 2275 Bayview Avenue, Toronto, M4N 3M6, Canada 
References:
[1] 
A. Ghenciu and R. D. Mauldin, Conformal graph directed Markov systems,, preprint, (). 
[2] 
R. D. Mauldin and M. Urbański, Dimensions and measures in infinite iterated function systems, Proc. London Math. Soc. (3), 73 (1996), 105154. doi: 10.1112/plms/s373.1.105. 
[3] 
R. D. Mauldin and M. Urbański, Conformal iterated function systems with applications to the geometry of continued fractions, Trans. Amer. Math. Soc., 351 (1999), 49955025. doi: 10.1090/S0002994799022680. 
[4] 
R. D. Mauldin and M. Urbański, "Graph Directed Markov Systems: Geometry and Dynamics of Limit Sets," Cambridge Tracts in Mathematics, 148, Cambridge University Press, Cambridge, 2003. 
[5] 
R. D. Mauldin and S. C. Williams, Hausdorff dimension in graph directed constructions, Trans. Amer. Math. Soc., 309 (1988), 811829. doi: 10.1090/S00029947198809616154. 
show all references
References:
[1] 
A. Ghenciu and R. D. Mauldin, Conformal graph directed Markov systems,, preprint, (). 
[2] 
R. D. Mauldin and M. Urbański, Dimensions and measures in infinite iterated function systems, Proc. London Math. Soc. (3), 73 (1996), 105154. doi: 10.1112/plms/s373.1.105. 
[3] 
R. D. Mauldin and M. Urbański, Conformal iterated function systems with applications to the geometry of continued fractions, Trans. Amer. Math. Soc., 351 (1999), 49955025. doi: 10.1090/S0002994799022680. 
[4] 
R. D. Mauldin and M. Urbański, "Graph Directed Markov Systems: Geometry and Dynamics of Limit Sets," Cambridge Tracts in Mathematics, 148, Cambridge University Press, Cambridge, 2003. 
[5] 
R. D. Mauldin and S. C. Williams, Hausdorff dimension in graph directed constructions, Trans. Amer. Math. Soc., 309 (1988), 811829. doi: 10.1090/S00029947198809616154. 
[1] 
Mario Roy, Mariusz Urbański. Random graph directed Markov systems. Discrete and Continuous Dynamical Systems, 2011, 30 (1) : 261298. doi: 10.3934/dcds.2011.30.261 
[2] 
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) : 235246. doi: 10.3934/dcds.2008.22.235 
[3] 
Mario Roy, Mariusz Urbański. Multifractal analysis for conformal graph directed Markov systems. Discrete and Continuous Dynamical Systems, 2009, 25 (2) : 627650. doi: 10.3934/dcds.2009.25.627 
[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) : 753766. doi: 10.3934/dcds.2020060 
[5] 
Welington Cordeiro, Manfred Denker, Michiko Yuri. A note on specification for iterated function systems. Discrete and Continuous Dynamical Systems  B, 2015, 20 (10) : 34753485. doi: 10.3934/dcdsb.2015.20.3475 
[6] 
Michael Jakobson, Lucia D. Simonelli. Countable Markov partitions suitable for thermodynamic formalism. Journal of Modern Dynamics, 2018, 13: 199219. doi: 10.3934/jmd.2018018 
[7] 
Manfred Denker, Yuri Kifer, Manuel Stadlbauer. Thermodynamic formalism for random countable Markov shifts. Discrete and Continuous Dynamical Systems, 2008, 22 (1&2) : 131164. doi: 10.3934/dcds.2008.22.131 
[8] 
Manfred Denker, Yuri Kifer, Manuel Stadlbauer. Corrigendum to: Thermodynamic formalism for random countable Markov shifts. Discrete and Continuous Dynamical Systems, 2015, 35 (1) : 593594. doi: 10.3934/dcds.2015.35.593 
[9] 
Yakov Pesin. On the work of Sarig on countable Markov chains and thermodynamic formalism. Journal of Modern Dynamics, 2014, 8 (1) : 114. doi: 10.3934/jmd.2014.8.1 
[10] 
Saisai Shi, Bo Tan, Qinglong Zhou. Best approximation of orbits in iterated function systems. Discrete and Continuous Dynamical Systems, 2021, 41 (9) : 40854104. doi: 10.3934/dcds.2021029 
[11] 
Hiroki Sumi, Mariusz Urbański. Bowen parameter and Hausdorff dimension for expanding rational semigroups. Discrete and Continuous Dynamical Systems, 2012, 32 (7) : 25912606. doi: 10.3934/dcds.2012.32.2591 
[12] 
L. Cioletti, E. Silva, M. Stadlbauer. Thermodynamic formalism for topological Markov chains on standard Borel spaces. Discrete and Continuous Dynamical Systems, 2019, 39 (11) : 62776298. doi: 10.3934/dcds.2019274 
[13] 
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) : 33413352. doi: 10.3934/dcds.2014.34.3341 
[14] 
David Cheban, Cristiana Mammana. Continuous dependence of attractors on parameters of nonautonomous dynamical systems and infinite iterated function systems. Discrete and Continuous Dynamical Systems, 2007, 18 (2&3) : 499515. doi: 10.3934/dcds.2007.18.499 
[15] 
Fernando J. SánchezSalas. Dimension of Markov towers for non uniformly expanding onedimensional systems. Discrete and Continuous Dynamical Systems, 2003, 9 (6) : 14471464. doi: 10.3934/dcds.2003.9.1447 
[16] 
Jialu Fang, Yongluo Cao, Yun Zhao. Measure theoretic pressure and dimension formula for nonergodic measures. Discrete and Continuous Dynamical Systems, 2020, 40 (5) : 27672789. doi: 10.3934/dcds.2020149 
[17] 
Peter Bella, Arianna Giunti. Green's function for elliptic systems: Moment bounds. Networks and Heterogeneous Media, 2018, 13 (1) : 155176. doi: 10.3934/nhm.2018007 
[18] 
Aline Cerqueira, Carlos Matheus, Carlos Gustavo Moreira. Continuity of Hausdorff dimension across generic dynamical Lagrange and Markov spectra. Journal of Modern Dynamics, 2018, 12: 151174. doi: 10.3934/jmd.2018006 
[19] 
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) : 58735903. doi: 10.3934/dcdsb.2021070 
[20] 
Ethan Akin. Good strategies for the Iterated Prisoner's Dilemma: Smale vs. Markov. Journal of Dynamics and Games, 2017, 4 (3) : 217253. doi: 10.3934/jdg.2017014 
2020 Impact Factor: 1.392
Tools
Metrics
Other articles
by authors
[Back to Top]