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1996 | 70 | 2 | 265-269

Tytuł artykułu

On continuous actions commutingwith actions of positive entropy

Treść / Zawartość

Języki publikacji

EN

Abstrakty

EN
Let F and G be finitely generated groups of polynomial growth with the degrees of polynomial growth d(F) and d(G) respectively. Let $S={S^f}_{f ∈ F}$ be a continuous action of F on a compact metric space X with a positive topological entropy h(S). Then (i) there are no expansive continuous actions of G on X commuting with S if d(G)

Rocznik

Tom

70

Numer

2

Strony

265-269

Daty

wydano
1996
otrzymano
1995-03-31
poprawiono
1995-09-07

Twórcy

  • Department of Mathematics, The Ohio State University, Columbus, Ohio 43210, U.S.A.

Bibliografia

  • [B] H. Bass, The degree of polynomial growth of finitely generated groups, Proc. London Math. Soc. 25 (1972), 603-614.
  • [BL] M. Boyle and D. Lind, Expansive subdynamics of $ℤ^n$ actions, to appear.
  • [F] A. Fathi, Expansiveness, hyperbolicity and Hausdorff dimension, Comm. Math. Phys. 126 (1989), 242-261.
  • [G] M. Gromov, Groups of polynomial growth and expanding maps, Publ. Math. IHES 53 (1981), 53-73.
  • [L] J. Lewowicz, Expansive homeomorphisms of surfaces, Bol. Soc. Brasil. Mat. 20 (1989), 113-133.
  • [M] R. Ma né, Expansive homeomorphisms, Trans. Amer. Math. Soc. 79 (1979), 312-319.
  • [MO] J. Moulin Ollagnier, Ergodic Theory and Statistical Mechanics, Lecture Notes in Math. 1115, Springer, New York, 1985.
  • [S] K. Schmidt, Automorphisms of compact abelian groups and affine varieties, Proc. London Math. Soc. 61 (1990), 480-496.
  • [Sh] M. Shereshevsky, Expansiveness, entropy and polynomial growth for groups acting on subshifts by automorphisms, Indag. Math. 3 (1993), 203-210.
  • [W] P. Walters, An Introduction to Ergodic Theory, Springer, New York, 1982.

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