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1999 | 162 | 1 | 1-36
Tytuł artykułu

On entropy of patterns given by interval maps

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Defining the complexity of a green pattern exhibited by an interval map, we give the best bounds of the topological entropy of a pattern with a given complexity. Moreover, we show that the topological entropy attains its strict minimum on the set of patterns with fixed eccentricity m/n at a unimodal X-minimal case. Using a different method, the last result was independently proved in[11].
Słowa kluczowe
Rocznik
Tom
162
Numer
1
Strony
1-36
Opis fizyczny
Daty
wydano
1999
otrzymano
1996-05-16
poprawiono
1997-10-27
poprawiono
1998-10-20
poprawiono
1999-03-13
Twórcy
autor
Bibliografia
  • [1] R. L. Adler, A. G. Konheim and M. H. McAndrew, Topological entropy, Trans. Amer. Math. Soc. 114 (1965), 309-319.
  • [2] L. Alsedà, J. Llibre and M. Misiurewicz, Combinatorial Dynamics and Entropy in Dimension One, Adv. Ser. Nonlinear Dynam. 5, World Sci., Singapore, 1993.
  • [3] L. Alsedà, J. Llibre and M. Misiurewicz, Periodic orbits of maps of Y, Trans. Amer. Math. Soc. 313 (1989), 475-538.
  • [4] S. Baldwin, Generalizations of a theorem of Sharkovskii on orbits of continuous real-valued functions, Discrete Math. 67 (1987), 111-127.
  • [5] A. Berman and R. J. Plemmons, Non-Negative Matrices in the Mathematical Sciences, Academic Press, New York, 1979.
  • [6] L. S. Block and W. A. Coppel, Dynamics in One Dimension, Lecture Notes in Math. 1513, Springer, Berlin, 1992.
  • [7] L. Block, J. Guckenheimer, M. Misiurewicz and L. S. Young, Periodic points and topological entropy of one dimensional maps, in: Global Theory of Dynamical Systems, Lecture Notes in Math. 819, Springer, Berlin, 1980, 18-34.
  • [8] A. Blokh, Rotation numbers, twists and a Sharkovskii-Misiurewicz-type order for patterns on the interval, Ergodic Theory Dynam. Systems 15 (1995), 1-14.
  • [9] A. Blokh, Functional rotation numbers for one dimensional maps, Trans. Amer. Math. Soc. 347 (1995), 499-514.
  • [10] A. Blokh, On rotation intervals for interval maps, Nonlinearity 7 (1994), 1395-1417.
  • [11] A. Blokh and M. Misiurewicz, Entropy of twist interval maps, Israel J. Math. 102 (1997), 61-99.
  • [12] J. Bobok and M. Kuchta, X-minimal patterns and generalization of Sharkovskii's theorem, Fund. Math. 156 (1998), 33-66.
  • [13] J. Bobok and I. Marek, On asymptotic behaviour of solutions of difference equations in partially ordered Banach spaces, submitted to Positivity.
  • [14] R. Bowen, Entropy for group endomorphisms and homogeneous spaces, Trans. Amer. Math. Soc. 153 (1971), 401-414.
  • [15] E. M. Coven and M. C. Hidalgo, On the topological entropy of transitive maps of the interval, Bull. Austral. Math. Soc. 44 (1991), 207-213.
  • [16] M. Denker, Ch. Grillenberger and K. Sigmund, Ergodic Theory on Compact Spaces, Lecture Notes in Math. 527, Springer, 1976.
  • [17] T. Fort, Finite Difference and Difference Equations in the Real Domain, Oxford Univ. Press, 1965.
  • [18] A. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, Encyclopedia Math. Appl. 54, Cambridge Univ. Press, 1995.
  • [19] M. Misiurewicz, Minor cycles for interval maps, Fund. Math. 145 (1994), 281-304.
  • [20] M. Misiurewicz and Z. Nitecki, Combinatorial patterns for maps of the interval, Mem. Amer. Math. Soc. 456 (1990).
  • [21] M. Misiurewicz and W. Szlenk, Entropy of piecewise monotone mappings, Studia Math. 67 (1980), 45-63.
  • [22] W. Parry, Symbolic dynamics and transformations of the unit interval, Trans. Amer. Math. Soc. 122 (1966), 368-378.
  • [23] W. Rudin, Real and Complex Analysis, McGraw-Hill, New York, 1974.
  • [24] P. Štefan, A theorem of Sharkovskii on the coexistence of periodic orbits of continuous endomorphisms of the real line, Comm. Math. Phys. 54 (1977), 237-248.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv162i1p1bwm
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