\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

Topological pressure and topological entropy of a semigroup of maps

Abstract Related Papers Cited by
  • By using the Carathéodory-Pesin structure(C-P structure), with respect to arbitrary subset, the topological pressure and topological entropy, introduced for a single continuous map, is generalized to the cases of semigroup of continuous maps. Several of their basic properties are provided.
    Mathematics Subject Classification: 37A35, 37B40.

    Citation:

    \begin{equation} \\ \end{equation}
  • [1]

    R. Adler, A. Konheim and M. McAndrew, Topological entropy, Trans. Amer. Math. Soc., 114 (1965), 303-319.doi: 10.1090/S0002-9947-1965-0175106-9.

    [2]

    L. Barreira, Y. Pesin and J. Schmeling, On a general concept of multifractality: Multifractal spectrum for dimensions, entropies and Lyapunv exponents, multifractal rigidity, Chaos, 7 (1997), 27-38.doi: 10.1063/1.166232.

    [3]

    A. Biś, Entropies of a semigroup of maps, Discrete Contin. Dyn. Systs. Series A., 11 (2004), 639-648.doi: 10.3934/dcds.2004.11.639.

    [4]

    A. Biś and M. Urbański, Some remarks on topological entropy of a semigroup of continuous maps, Cubo, 8 (2006), 63-71.

    [5]

    A. Biś and P. Walczak, Entropies of hyperbolic groups and some foliated spaces, in "Foliations-Geometry and Dynamics" (eds. P. Walczak et al. ), World Sci. Publ., Singapore, (2002), 197-211.

    [6]

    R. Bowen, Entropy for group endomorphisms and homogenous spaces, Trans. Amer. Math. Soc., 153 (1971), 401-414.doi: 10.1090/S0002-9947-1971-0274707-X.

    [7]

    R. Bowen, Topological entropy for non-compact sets, Trans. Amer. Math. Soc., 184 (1973), 125-136.doi: 10.1090/S0002-9947-1973-0338317-X.

    [8]

    C. Carathéodory, Über das lineare mass, Göttingen Nachr, (1914), 406-426.

    [9]

    E. I. Dinaburg, The relation between topological entropy and metric entropy, Soviet Math. Dokl., 11 (1970), 13-16.

    [10]

    S. Friedland, Entropy of graphs,semigroups and groups, in "Ergodic Theory of $Z^d$ Actions" (eds. M. Policott and K. Schmidt), London Math. Soc, London, (1996), 319-343.

    [11]

    E. Ghys, R. Langevin and P. Walczak, Entropie geometrique des feuilletages, Acta Math., 160 (1988), 105-142.doi: 0.1007/BF02392274.

    [12]

    M. Hurley, On topological entropy of maps, Ergodic Th. and Dynam. Sys., 15 (1995), 557-568.

    [13]

    R. Langevin and F. Przytycki, Entropie de l'image inverse d'une application, Bull. Soc. Math. France., 120 (1992), 237-250.

    [14]

    R. Langevin and P. Walczak, Entropie d'une dynamique, C. R. Acad. Sci. Paris, Ser I, 312 (1991), 141-144.

    [15]

    Z. Nitecki and F. Przytycki, Preimage entropy for mapping, Internat. J. Bifur. Chaos Appl. Sci. Engrg, 9 (1999), 1815-1843.doi: 10.1142/S0218127499001309.

    [16]

    Y. Pesin, "Dimension Theory in Dynamical Systems," Chicago: The university of Chicago Press, 1997.

    [17]

    Y. Pesin and B. Pitskel, Topological pressure and the variational principle for non-compact sets, Functional Anal. and Its Applications, 18 (1984), 50-63.doi: 10.1007/BF01083692.

    [18]

    D. Ruelle, "Thermodynamic Formalism," Addison-Wesley, Reading, MA,1978.

    [19]

    P. Walters, A variational principle for the pressure of continuous transformations, Amer. J. Math., 97 (1975), 937-971.doi: 10.2307/2373682.

  • 加载中
SHARE

Article Metrics

HTML views() PDF downloads(169) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return