On continuous actions commutingwith actions of positive entropy

Mark Shereshevsky

Colloquium Mathematicae (1996)

  • Volume: 70, Issue: 2, page 265-269
  • ISSN: 0010-1354

Abstract

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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)

How to cite

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Shereshevsky, Mark. "On continuous actions commutingwith actions of positive entropy." Colloquium Mathematicae 70.2 (1996): 265-269. <http://eudml.org/doc/210411>.

@article{Shereshevsky1996,
abstract = {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)},
author = {Shereshevsky, Mark},
journal = {Colloquium Mathematicae},
keywords = {expansive homeomorphisms; degrees of polynomial growth; compact metric space; expansive continuous action; positive topological entropy},
language = {eng},
number = {2},
pages = {265-269},
title = {On continuous actions commutingwith actions of positive entropy},
url = {http://eudml.org/doc/210411},
volume = {70},
year = {1996},
}

TY - JOUR
AU - Shereshevsky, Mark
TI - On continuous actions commutingwith actions of positive entropy
JO - Colloquium Mathematicae
PY - 1996
VL - 70
IS - 2
SP - 265
EP - 269
AB - 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)
LA - eng
KW - expansive homeomorphisms; degrees of polynomial growth; compact metric space; expansive continuous action; positive topological entropy
UR - http://eudml.org/doc/210411
ER -

References

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  1. [B] H. Bass, The degree of polynomial growth of finitely generated groups, Proc. London Math. Soc. 25 (1972), 603-614. Zbl0259.20045
  2. [BL] M. Boyle and D. Lind, Expansive subdynamics of ℤ n actions, to appear. 
  3. [F] A. Fathi, Expansiveness, hyperbolicity and Hausdorff dimension, Comm. Math. Phys. 126 (1989), 242-261. Zbl0819.58026
  4. [G] M. Gromov, Groups of polynomial growth and expanding maps, Publ. Math. IHES 53 (1981), 53-73. Zbl0474.20018
  5. [L] J. Lewowicz, Expansive homeomorphisms of surfaces, Bol. Soc. Brasil. Mat. 20 (1989), 113-133. Zbl0753.58022
  6. [M] R. Ma né, Expansive homeomorphisms, Trans. Amer. Math. Soc. 79 (1979), 312-319. 
  7. [MO] J. Moulin Ollagnier, Ergodic Theory and Statistical Mechanics, Lecture Notes in Math. 1115, Springer, New York, 1985. Zbl0558.28010
  8. [S] K. Schmidt, Automorphisms of compact abelian groups and affine varieties, Proc. London Math. Soc. 61 (1990), 480-496. Zbl0789.28013
  9. [Sh] M. Shereshevsky, Expansiveness, entropy and polynomial growth for groups acting on subshifts by automorphisms, Indag. Math. 3 (1993), 203-210. Zbl0794.28010
  10. [W] P. Walters, An Introduction to Ergodic Theory, Springer, New York, 1982. Zbl0475.28009

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