EQUILIBRIUM STATES AND INVARIANT MEASURES FOR RANDOM DYNAMICAL SYSTEMS

被引:0
作者
Werner, Ivan
机构
[1] Udal'tsov Street 55, Moscow
关键词
Equilibrium states; random dynamical systems; Markov partitions; contractive Markov systems; Markov operators; THERMODYNAMIC FORMALISM; MARKOV-PROCESSES; SHIFTS;
D O I
10.3934/dcds.2015.35.1285
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Random dynamical systems with countably many maps which admit countable Markov partitions on complete metric spaces such that the resulting Markov systems are uniformly continuous and contractive are considered. A non-degeneracy and a consistency conditions for such systems, which admit some proper Markov partitions of connected spaces, are introduced, and further sufficient conditions for them are provided. It is shown that every uniformly continuous Markov system associated with a continuous random dynamical system is consistent if it has a dominating Markov chain. A necessary and sufficient condition for the existence of an invariant Borel probability measure for such a non-degenerate system with a dominating Markov chain and a finite (16) is given. The condition is also sufficient if the non-degeneracy is weakened with the consistency condition. A further sufficient condition for the existence of an invariant measure for such a consistent system which involves only the properties of the dominating Markov chain is provided. In particular, it implies that every such a consistent system with a finite Markov partition and a finite (16) has an invariant Borel probability measure. A bijective map between these measures and equilibrium states associated with such a system is established in the non-degenerate case. Some properties of the map and the measures are given.
引用
收藏
页码:1285 / 1326
页数:42
相关论文
共 50 条
  • [21] Random Dynamical Systems with Inputs
    de Freitas, Michael Marcondes
    Sontag, Eduardo D.
    NONAUTONOMOUS DYNAMICAL SYSTEMS IN THE LIFE SCIENCES, 2013, 2102 : 41 - 87
  • [22] Continuous random dynamical systems
    Horbacz, Katarzyna
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2013, 408 (02) : 623 - 637
  • [23] Random dynamical systems: a review
    Rabi Bhattacharya
    Mukul Majumdar
    Economic Theory, 2003, 23 : 13 - 38 (2004)
  • [24] Synchronization rates and limit laws for random dynamical systems
    Gelfert, Katrin
    Salcedo, Graccyela
    MATHEMATISCHE ZEITSCHRIFT, 2024, 308 (01)
  • [25] First return maps of random maps and invariant measures
    Inoue, Tomoki
    NONLINEARITY, 2020, 33 (01) : 249 - 275
  • [26] APPROXIMATION OF INVARIANT FOLIATIONS FOR STOCHASTIC DYNAMICAL SYSTEMS
    Sun, Xu
    Kan, Xingye
    Duan, Jinqiao
    STOCHASTICS AND DYNAMICS, 2012, 12 (01)
  • [27] Random chain recurrent sets for random dynamical systems
    Chen, Xiaopeng
    Duan, Jinqiao
    DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, 2009, 24 (04): : 537 - 546
  • [28] Distributional chaos in random dynamical systems
    Kovac, Jozef
    Jankova, Katarina
    JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2019, 25 (04) : 455 - 480
  • [29] Holder conjugacies for random dynamical systems
    Barreira, Luis
    Valls, Claudia
    PHYSICA D-NONLINEAR PHENOMENA, 2006, 223 (02) : 256 - 269
  • [30] Hitting times for random dynamical systems
    Arbieto, Alexander
    Junqueira, Andre
    Soares, Regis
    DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, 2013, 28 (04): : 484 - 500