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Equilibrium states and invariant measures for random dynamical systems
1. | Udal'tsov Street 55, Apt. 17, Moscow, 119454, Russian Federation |
References:
[1] |
A. Baraviera, C. F. Lardizabal, A. O. Lopes and M. Terra Cunha, A dynamical point of view of Quantum Information: Entropy, pressure and Wigner measures, in Dynamics, Games and Science II, Springer Proceedings in Mathematics, 2 (2011), 161-185.
doi: 10.1007/978-3-642-14788-3_13. |
[2] |
M. F. Barnsley, S. G. Demko, J. H. Elton and J. S. Geronimo, Invariant measure for Markov processes arising from iterated function systems with place-dependent probabilities, Ann. Inst. Henri Poincaré, 24 (1988), 367-394. |
[3] |
M. F. Barnsley, S. G. Demko, J. H. Elton and J. S. Geronimo, Erratum: Invariant measure for Markov processes arising from iterated function systems with place-dependent probabilities, Ann. Inst. Henri Poincaré, 25 (1989), 589-590. |
[4] |
V. I. Bogachev, Measure Theory. Vol. I,II. Springer, 2007.
doi: 10.1007/978-3-540-34514-5. |
[5] |
M. Denker and M. Urbański, On the existence of conformal measures, Trans. Am. Math. Soc., 328 (1991), 563-587.
doi: 10.1090/S0002-9947-1991-1014246-4. |
[6] |
H. Föllmer, U. Horst and A. Kirman, Equilibria in financial markets with heterogeneous agents: A probabilistic perspective, Journal of Mathematical Economics, 41 (2005), 123-155.
doi: 10.1016/j.jmateco.2004.08.001. |
[7] |
K. Horbacz and T. Szarek, Irreducible Markov systems on Polish spaces, Studia Math., 177 (2006), 285-295.
doi: 10.4064/sm177-3-7. |
[8] |
R. Isaac, Markov processes and unique stationary probability measures, Pacific J. Math., 12 (1962), 273-286.
doi: 10.2140/pjm.1962.12.273. |
[9] |
A. Johansson, A. Öberg and M. Pollicott, Countable state shifts and uniqueness of g-measures, Amer. J. Math., 129 (2007), 1501-1511.
doi: 10.1353/ajm.2007.0044. |
[10] |
M. Keane, Strongly Mixing $g$-Measures, Inventiones math., 16 (1972), 309-324.
doi: 10.1007/BF01425715. |
[11] |
F. Ledrappier, Principe variationnel et systèmes dynamiques symboliques, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 30 (1974), 185-202.
doi: 10.1007/BF00533471. |
[12] |
O. Sarig, Thermodynamic formalism for countable Markov shifts, Ergod. Th. & Dynam. Sys., 19 (1999), 1565-1593.
doi: 10.1017/S0143385799146820. |
[13] |
O. Sarig, Thermodynamic formalism for null recurrent potentials, Israel Journal of Mathematics, 121 (2001), 285-311.
doi: 10.1007/BF02802508. |
[14] |
W. Slomczynski, Dynamical Entropy, Markov Operators, and Iterated Function Systems, Rozprawy Habilitacyjne Uniwersytetu Jagiellońskiego Nr 362, Wydawnictwo Uniwersytetu Jagiellońskiego, Kraków, 2003. |
[15] |
T. Szarek, Invariant measures for nonexpansive Markov operators on Polish spaces, Diss. Math., 415 (2003), 1-62.
doi: 10.4064/dm415-0-1. |
[16] |
P. Walters, Ruelle's Operator Theorem and $g$-measures, Tran. AMS, 214 (1975), 375-387.
doi: 10.1090/S0002-9947-1975-0412389-8. |
[17] |
I. Werner, Contractive Markov systems, J. London Math. Soc., 71 (2005), 236-258.
doi: 10.1112/S0024610704006088. |
[18] |
I. Werner, Coding map for a contractive Markov system, Math. Proc. Camb. Phil. Soc., 140 (2006), 333-347.
doi: 10.1017/S0305004105009072. |
[19] |
I. Werner, The generalized Markov measure as an equilibrium state, Nonlinearity 18 (2005), 2261-2274.
doi: 10.1088/0951-7715/18/5/019. |
[20] |
I. Werner, Dynamically defined measures and equilibrium states, J. Math. Phys. 52 (2011), 122701, 17 pp.
doi: 10.1063/1.3666020. |
[21] |
I. Werner, Erratum: Dynamically defined measures and equilibrium states, J. Math. Phys. 53 (2012), 079902, 2 pp.
doi: 10.1063/1.4736999. |
[22] |
I. Werner, Contractive Markov systems II,, , ().
|
[23] |
I. Werner, Fundamental Markov systems,, , ().
|
show all references
References:
[1] |
A. Baraviera, C. F. Lardizabal, A. O. Lopes and M. Terra Cunha, A dynamical point of view of Quantum Information: Entropy, pressure and Wigner measures, in Dynamics, Games and Science II, Springer Proceedings in Mathematics, 2 (2011), 161-185.
doi: 10.1007/978-3-642-14788-3_13. |
[2] |
M. F. Barnsley, S. G. Demko, J. H. Elton and J. S. Geronimo, Invariant measure for Markov processes arising from iterated function systems with place-dependent probabilities, Ann. Inst. Henri Poincaré, 24 (1988), 367-394. |
[3] |
M. F. Barnsley, S. G. Demko, J. H. Elton and J. S. Geronimo, Erratum: Invariant measure for Markov processes arising from iterated function systems with place-dependent probabilities, Ann. Inst. Henri Poincaré, 25 (1989), 589-590. |
[4] |
V. I. Bogachev, Measure Theory. Vol. I,II. Springer, 2007.
doi: 10.1007/978-3-540-34514-5. |
[5] |
M. Denker and M. Urbański, On the existence of conformal measures, Trans. Am. Math. Soc., 328 (1991), 563-587.
doi: 10.1090/S0002-9947-1991-1014246-4. |
[6] |
H. Föllmer, U. Horst and A. Kirman, Equilibria in financial markets with heterogeneous agents: A probabilistic perspective, Journal of Mathematical Economics, 41 (2005), 123-155.
doi: 10.1016/j.jmateco.2004.08.001. |
[7] |
K. Horbacz and T. Szarek, Irreducible Markov systems on Polish spaces, Studia Math., 177 (2006), 285-295.
doi: 10.4064/sm177-3-7. |
[8] |
R. Isaac, Markov processes and unique stationary probability measures, Pacific J. Math., 12 (1962), 273-286.
doi: 10.2140/pjm.1962.12.273. |
[9] |
A. Johansson, A. Öberg and M. Pollicott, Countable state shifts and uniqueness of g-measures, Amer. J. Math., 129 (2007), 1501-1511.
doi: 10.1353/ajm.2007.0044. |
[10] |
M. Keane, Strongly Mixing $g$-Measures, Inventiones math., 16 (1972), 309-324.
doi: 10.1007/BF01425715. |
[11] |
F. Ledrappier, Principe variationnel et systèmes dynamiques symboliques, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 30 (1974), 185-202.
doi: 10.1007/BF00533471. |
[12] |
O. Sarig, Thermodynamic formalism for countable Markov shifts, Ergod. Th. & Dynam. Sys., 19 (1999), 1565-1593.
doi: 10.1017/S0143385799146820. |
[13] |
O. Sarig, Thermodynamic formalism for null recurrent potentials, Israel Journal of Mathematics, 121 (2001), 285-311.
doi: 10.1007/BF02802508. |
[14] |
W. Slomczynski, Dynamical Entropy, Markov Operators, and Iterated Function Systems, Rozprawy Habilitacyjne Uniwersytetu Jagiellońskiego Nr 362, Wydawnictwo Uniwersytetu Jagiellońskiego, Kraków, 2003. |
[15] |
T. Szarek, Invariant measures for nonexpansive Markov operators on Polish spaces, Diss. Math., 415 (2003), 1-62.
doi: 10.4064/dm415-0-1. |
[16] |
P. Walters, Ruelle's Operator Theorem and $g$-measures, Tran. AMS, 214 (1975), 375-387.
doi: 10.1090/S0002-9947-1975-0412389-8. |
[17] |
I. Werner, Contractive Markov systems, J. London Math. Soc., 71 (2005), 236-258.
doi: 10.1112/S0024610704006088. |
[18] |
I. Werner, Coding map for a contractive Markov system, Math. Proc. Camb. Phil. Soc., 140 (2006), 333-347.
doi: 10.1017/S0305004105009072. |
[19] |
I. Werner, The generalized Markov measure as an equilibrium state, Nonlinearity 18 (2005), 2261-2274.
doi: 10.1088/0951-7715/18/5/019. |
[20] |
I. Werner, Dynamically defined measures and equilibrium states, J. Math. Phys. 52 (2011), 122701, 17 pp.
doi: 10.1063/1.3666020. |
[21] |
I. Werner, Erratum: Dynamically defined measures and equilibrium states, J. Math. Phys. 53 (2012), 079902, 2 pp.
doi: 10.1063/1.4736999. |
[22] |
I. Werner, Contractive Markov systems II,, , ().
|
[23] |
I. Werner, Fundamental Markov systems,, , ().
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