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Tytuł artykułu

Mixing properties of nearly maximal entropy measures for $ℤ^{d}$ shifts of finite type

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We prove that for a certain class of $ℤ^d$ shifts of finite type with positive topological entropy there is always an invariant measure, with entropy arbitrarily close to the topological entropy, that has strong metric mixing properties. With the additional assumption that there are dense periodic orbits, one can ensure that this measure is Bernoulli.
Słowa kluczowe
Rocznik
Tom
Numer
1
Strony
43-50
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-04-25
poprawiono
1999-12-10
Twórcy
  • Department of Mathematics, George Washington University, Washington, DC 20052, U.S.A.
  • Department of Mathematics, North Dakota State University, Fargo, ND 58105, U.S.A.
Bibliografia
  • [1] R. Burton and J. E. Steif, Non-uniqueness of measures of maximal entropy for subshifts of finite type, Ergodic Theory Dynam. Systems 14 (1994), 213-235.
  • [2] R. Burton and J. E. Steif, Some $2$-d symbolic dynamical systems: entropy and mixing, in: Ergodic Theory of $ℤ^d$ Actions (Warwick, 1993-1994), London Math. Soc. Lecture Note Ser. 228, Cambridge Univ. Press, Cambridge, 1996, 297-305.
  • [3] A. Fieldsteel and N. A. Friedman, Restricted orbit changes of ergodic $ℤ^d$-actions to achieve mixing and completely positive entropy, Ergodic Theory Dynam. Systems 6 (1986), 505-528.
  • [4] H R. J. Hasfura-Buenaga, The equivalence theorem for $ℤ^d$-actions of positive entropy, ibid. 12 (1992), 725-741.
  • [5] A. del Junco and D. J. Rudolph, Kakutani equivalence of ergodic $ℤ^n$ actions, ibid. 4 (1984), 89-104.
  • [6] F. Ledrappier, Un champ markovien peut être d'entropie nulle et mélangeant, C. R. Acad. Sci. Paris Sér. A 287 (1978), 561-563.
  • [7] M. Misiurewicz, A short proof of the variational principle for a $ℤ_{+}^{N}$ action on a compact space, Astérisque 40 (1976), 147-157.
  • [8] S. Mozes, A zero entropy, mixing of all orders tiling system, in: Symbolic Dynamics and its Applications (New Haven, CT, 1991), Amer. Math. Soc., Providence, RI, 1992, 319-325.
  • [9] E. A. Robinson, Jr. and A. A. Şahin, On the absence of invariant measures with locally maximal entropy for a class of $ℤ^d$ shifts of finite type, Proc. Amer. Math. Soc., to appear.
  • [10] E. A. Robinson, Modeling ergodic measure preserving actions on $ℤ^d$ shifts of finite type, preprint, 1998.
  • [11] T. Ward, Automorphisms of $ℤ^d$-subshifts of finite type, Indag. Math. (N.S.) 5 (1994), 495-504.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-cmv84i1p43bwm
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