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Exponential Convergence For Markov Systems

References [1] Barnsley M.F., Demko S.G., Elton J.H., Geronimo J.S., Invariant measures for Markov processes arising from iterated function systems with place dependent probabilities , Ann. Inst. H. Poincaré Probab. Statist. 24 (1988), 367–394. [2] Hairer M., Exponential mixing properties of stochastic PDEs through asymptotic coupling , Probab. Theory Related Fields 124 (2002), 345–380. [3] Hairer M., Mattingly J., Scheutzow M., Asymptotic coupling and a general form of Harris’ theorem with applications to stochastic delay equations

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On the metrical theory of a non-regular continued fraction expansion

References [1] Adams, W.W. and Davison, J.L., A remarkable class of continued fractions, Proc. Amer. Math. Soc. 65 (1977) 194-198. [2] Boyarsky, A. and Góra, P., Laws of Chaos: Invariant Measures and Dynamical Systems in One Dimension, Birkhäuser, Boston, 1997. [3] Brezinski, C., History of Continued Fractions and Padé Approximants. Springer Series in Computational Mathematics 12, Springer-Verlag, Berlin, 1991. [4] Corless, R.M., Continued fractions and chaos, Amer. Math. Monthly 99(3) (1992

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Numerical investigation on global dynamics for nonlinear stochastic heat conduction via global random attractors theory

said to be global random point attractor . Actually, Definition 2.3 is the notion of random attractor for RDS, if omit 0 in S (0, s , ω ) in definition of random attractors for SDS proposed in Ref [ 4 ], random attractor for RDS and for SDS are the same. The follow assertion provides the relationship between random attractors and invariant measures which is important to exploit the numerical results to expound the global dynamics for RDS. Proposition 2.4 When the RDS or SDS φ possesses global random attractor comply with Definition 2.3 , by the

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Random Dynamical Systems with Jumps and with a Function Type Intensity

References [1] Davis M.H.A., Markov Models and Optimization , Chapman and Hall, London, 1993. [2] Diekmann O., Heijmans H.J., Thieme H.R., On the stability of the cells size distribution , J. Math. Biol. 19 (1984), 227–248. [3] Horbacz K., Asymptotic stability of a system of randomly connected transformations on Polish spaces , Ann. Polon. Math. 76 (2001), 197–211. [4] Horbacz K., Invariant measures for random dynamical systems , Dissertationes Math. 451 (2008), 68 pp. [5] Kazak J., Piecewise-deterministic Markov processes

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Ergodic theory approach to chaos: Remarks and computational aspects

Koopman, B. O. (1932). Recent contributions to the ergodic theory, Mathematics: Proceedings of the National Academy of Sciences   18 : 279-282. Bronsztejn, I. N., Siemiendiajew, K. A., Musiol, G. and Muhlig, H. (2004). Modern Compendium of Mathematics , PWN, Warsaw, (in Polish, translation from German). Dawidowicz, A. L. (1992). On invariant measures supported on the compact sets II, Universitatis Iagellonicae Acta Mathematica   29 : 25-28. Dawidowicz, A. L. (1992). A method of construction

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On some Transformations of Fuzzy Measures

References [1] MESIAR, R.-BORKOTOKEY, S.-LESHANG, J.-KALINA, M.: Aggregation functions and capacities, Fuzzy Sets Syst. 2017 (submitted). [2] BORKOTOKEY, S.-KOMORN´IKOV´A, M.-LI, J.-MESIAR, R.: Aggregation functions, similarity and fuzzy measures, in: Proc. of the Internat. Summer School on Aggregation Operators-AGOP’17 (V. Torra et all., eds.), Skovde, Sveden, Advances in Intelligent Systems and Computing, Vol. 581, Springer, Cham, 2017, pp. 223-228.

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The island model as a Markov dynamic system

, T., Fogel, D. and Michalewicz, Z. (2000). Evolutionary Computation: Basic Algorithms and Operators , Vols. 1 and 2, Institute of Physics Publishing, Bristol/Philadelphia, PA . Back, T., Hammel, U. and Schwefel, H.-P. (1997). Evolutionary computation: Comments on the history and current state, IEEE Transactions on Evolutionary Computation 1 (1): 3-17. Billingsley, P. (1995). Probability and Measure , Wiley-Interscience, Hoboken, NJ. Brabazon, A. and O’Neill, M. (2006). Biologically Inspired Algorithms for

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Strong Unique Ergodicity of Random Dynamical Systems on Polish Spaces

stability of Markov operators on Polish spaces , Studia Math. 143 (2000), 145–152. [6] Szarek T., Invariant measures for non-expansive Markov operators on Polish spaces , Dissertationes Math. 415 (2003), 62 pp. [7] Valadier M., Young measures , in: Methods of Nonconvex Analysis (Varrenna 1989) , Lecture Notes in Math. 1446, Springer, Berlin, 1990, pp. 152–188.

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Pointwise Density Topology with Respect to Admissible σ-Algebras

References [1] CIESIELSKI, K.-LARSON, L.-OSTASZEWSKI, K.: I-density continuous functions , Mem. Amer. Math. Soc. 107 (1994), pp. 133. [2] GÓRAJSKA, M.: Pointwise density topology , Cent. Eur. J. Math., 2013 (submitted). [3] GÓRAJSKA, M.-WILCZYŃSKI, W.: Density topology generated by the convergence everywhere except for a finite set , Demonstratio Math. 46 (2013), 197-208. [4] HEJDUK, J.: On density topologies with respect to invariant σ-ideals , J. Appl. Anal. 8 (2002), 201

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Multi Ping-Pong and an Entropy Estimate in Groups

. [6] Langevin R., Walczak P., Some invariants measuring dynamics of codimension-one foliations, in: T. Mizutani et al. (Eds.), Geometric study of foliations,World Sci. Publ., Singapore, 1994, pp. 345-358. [7] Llibre J., Misiurewicz M., Horseshoes, entropy and periods for graph maps, Topology 32 (1993), 649-664. [8] Shi E., Wang S., The ping-pong game, geometric entropy and expansiveness for group actions on Peano continua having free dendrites, Fund. Math. 203 (2009), 21-37. [9] Tarchała K., Walczak P., Ping-pong and

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