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Expansive Measures of Nonautonomous Iterated Function Systems

  • Mengxin Cui [1] ; Bilel Selmi [2] ; Zhiming Li [3]
    1. [1] Beijing University of Posts and Telecommunications

      Beijing University of Posts and Telecommunications

      China

    2. [2] University of Monastir

      University of Monastir

      Túnez

    3. [3] Northwest University

      Northwest University

      China

  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 2, 2025
  • Idioma: inglés
  • Enlaces
  • Resumen
    • In this paper, we explore expansive measures and expansiveness within the context of nonautonomous iterated function systems. Specifically, we demonstrate that the set of expansive measures for any nonautonomous iterated function system forms a Gδσ subset of the set of all Borel measures.

  • Referencias bibliográficas
    • 1. Barnsley, M.: Fractals everywhere. Academic Press, Inc., Boston, MA, 1988. xii+396 pp. ISBN:0-12- 079062-9
    • 2. Freitas, A.C.M., Freitas, J.M., Vaienti, S.: Extreme value laws for non stationary processes generated by sequential and random dynamical...
    • 3. Kolyada, S., Snoha, L.: Topological entropy of nonautonomous dynamical systems. Random Comput. Dynam. 4(2–3), 205–233 (1996)
    • 4. Muentes, A., de Jeovanny, J.: On the continuity of the topological entropy of non-autonomous dynamical systems. Bull. Braz. Math. Soc....
    • 5. Stadlbauer, M.: Coupling methods for random topological Markov chains. Ergodic Theory Dynam. Syst. 37(3), 971–994 (2017)
    • 6. Yokoi, K.: Recurrence properties of a class of nonautonomous discrete systems. Bull. Belg. Math. Soc. Simon Stevin 20(4), 689–705 (2013)
    • 7. Kloeden, P.E.: Nonautonomous attractors of switching systems. Dyn. Syst. 21(2), 209–230 (2006)
    • 8. Kloeden, P.E.: Synchronization of nonautonomous dynamical systems. Electron. J. Differential Equations (39), 10 pp (2003)
    • 9. Rasmussen, M., et al.: Transit times and mean ages for nonautonomous and autonomous compartmental systems. J. Math. Biol. 73(6–7), 1379–1398...
    • 10. Utz, W.R.: Unstable homeomorphisms. Proc. Amer. Math. Soc. 1, 769–774 (1950)
    • 11. Bowen, R., Walters, P.: Expansive one-parameter flows. J. Differ. Equ. 12, 180–193 (1972)
    • 12. Artigue, A., Carrasco-Olivera, D.: A note on measure-expansive diffeomorphisms. J. Math. Anal. Appl. 428(1), 713–716 (2015)
    • 13. Carrasco-Olivera, D., Morales, C.A.: Expansive measures for flows. J. Differ. Equ. 256(7), 2246–2260 (2014)
    • 14. Morales, C.A.: On the complexity of expansive measures. Acta Math. Sin. 31(9), 1501–1507 (2015)
    • 15. Norton, V., O’Brien, T.: Anosov flows and expansiveness. Proc. Amer. Math. Soc. 40, 625–628 (1973)
    • 16. Ruggiero, R.O.: Expansive dynamics and hyperbolic geometry. Bol. Soc. Brasil. Mat. 25(2), 139–172 (1994)
    • 17. Lewowicz, J., Cerminara, M.: Some open problems concerning expansive systems. Rend. Istit. Mat. Univ. Trieste. 42, 129–141 (2010)
    • 18. Arbieto, A., Morales, C.A.: Some properties of positive entropy maps. Ergodic Theory Dynam. Syst. 34(3), 765–776 (2014)
    • 19. Morales, C.A., Sirvent, V.: Expansivity for measures on uniform spaces. Trans. Amer. Math. Soc. 368(8), 5399–5414 (2016)
    • 20. Arbieto, A.: Periodic orbits and expansiveness. Math. Z. 269(3–4), 801–807 (2011)
    • 21. Arbieto, A., Morales, C.A.: Expansive measures. Publ. Mat. Urug. 14, 61–71 (2013)
    • 22. Fornaess, J.E., Mihailescu, E.: Equilibrium measures on saddle sets of holomorphic maps on P2. Math. Ann. 356, 1471–1491 (2013)
    • 23. Lee, K., Morales, C.A.: Topological stability and pseudo-orbit tracing property for expansive measures. J. Differ. Equ. 262(6), 3467–3487...
    • 24. Lee, K., Morales, C.A., Shin, B.: On the set of expansive measures. Commun. Contemp. Math. 20(7), 1750086, 10 pp.(2018)
    • 25. Morales, C.: A generalization of expansivity. Discrete Contin. Dyn. Syst. 32(1), 293–301 (2012)
    • 26. Morales, C.A., Sirvent, V.: Expansive measures. IMPA Mathematical Publications, (2013)
    • 27. Mihailescu, E.: Higher dimensional expanding maps and toral extensions. Proc. Amer. Math. Soc. 141(10), 3467–3475 (2013)
    • 28. Eisenberg, M.: Expansive transformation semigroups of endomorphisms. Fund. Math. 59, 313–321 (1966)
    • 29. Liu, B.G., Tang, Y.J.,Ma, D.K.: On the complexity of expansive measures of nonautonomous dynamical systems. Bull. Malays. Math. Sci. Soc....
    • 30. Liu, B.G., Tang, Y.J., Ma, D.K.: A note on the expansive measures of nonautonomous dynamical systems. Bull. Malays. Math. Sci. Soc. 45(5),...
    • 31. Rempe-Gillen, L., Urban´ski, M.: Non-autonomous conformal iterated function systems and Moran-set constructions. Trans. Amer. Math. Soc....
    • 32. Billingsley, P.: Convergence of probability measures. A Wiley-Interscience Publication, (1999)
    • 33. K.R.: Parthasarathy. Probability measures on metric spaces. Academic Press, (1967)
    • 34. Sears, M.: Expansive self-homeomorphisms of the Cantor set. Math. Syst. Theory 6, 129–132 (1972)
    • 35. Mursaleen, M., Mohiuddine, S.A.: Convergence Methods for Double Sequences and Applications. Springer, (2014)
    • 36. Walters, P.: An Introduction to Ergodic Theory. Springer, (2013)
    • 37. Parthasarathy, K.R., Ranga Rao, R., Varadhan, S.R.S.: On the category of indecomposable distributions on topological groups. Trans. Amer....
    • 38. Lenz, D., Stollmann, P.: Generic sets in spaces of measures and generic singular continuous spectrum for Delone Hamiltonians. Duke Math....
    • 39. Kuratowski, K.: Topology. A. Kirkor Academic Press, (1968)
    • 40. Lasota, A., Myjak, J.: Markov operators and fractals. Bull. Polish Acad. Sci. Math. 45(2), 197-C210 (1997)
    • 41. Lasota, A., Myjak, J.: Attractors of multifunctions. Bull. Polish Acad. Sci. Math. 48(3), 319-C334 (2000)
    • 42. Hutchinson, J.E.: Fractals and self-similarity. Indiana Univ. Math. J. 30(5), 713–747 (1981)
    • 43. Zhou, Z.L.: Weakly almost periodic point and measure center. Sci. China Math. 2, 12 (1993)
    • 44. Barnsley, M.: Fractals everywhere. Academic Press, Inc., Boston, MA, 1988. xii+396 pp. ISBN:0-12- 079062-9

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