On continuous actions commutingwith actions of positive entropy
Shereshevsky, Mark
Colloquium Mathematicae, Tome 70 (1996), p. 265-269 / Harvested from The Polish Digital Mathematics Library
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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=Sff∈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)

Publié le : 1996-01-01
EUDML-ID : urn:eudml:doc:210411 
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Shereshevsky, Mark. On continuous actions commutingwith actions of positive entropy. Colloquium Mathematicae, Tome 70 (1996) pp. 265-269. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv70i2p265bwm/

[000] [B] H. Bass, The degree of polynomial growth of finitely generated groups, Proc. London Math. Soc. 25 (1972), 603-614. | Zbl 0259.20045

[001] [BL] M. Boyle and D. Lind, Expansive subdynamics of ℤn actions, to appear.

[002] [F] A. Fathi, Expansiveness, hyperbolicity and Hausdorff dimension, Comm. Math. Phys. 126 (1989), 242-261. | Zbl 0819.58026

[003] [G] M. Gromov, Groups of polynomial growth and expanding maps, Publ. Math. IHES 53 (1981), 53-73. | Zbl 0474.20018

[004] [L] J. Lewowicz, Expansive homeomorphisms of surfaces, Bol. Soc. Brasil. Mat. 20 (1989), 113-133. | Zbl 0753.58022

[005] [M] R. Ma né, Expansive homeomorphisms, Trans. Amer. Math. Soc. 79 (1979), 312-319.

[006] [MO] J. Moulin Ollagnier, Ergodic Theory and Statistical Mechanics, Lecture Notes in Math. 1115, Springer, New York, 1985. | Zbl 0558.28010

[007] [S] K. Schmidt, Automorphisms of compact abelian groups and affine varieties, Proc. London Math. Soc. 61 (1990), 480-496. | Zbl 0789.28013

[008] [Sh] M. Shereshevsky, Expansiveness, entropy and polynomial growth for groups acting on subshifts by automorphisms, Indag. Math. 3 (1993), 203-210. | Zbl 0794.28010

[009] [W] P. Walters, An Introduction to Ergodic Theory, Springer, New York, 1982. | Zbl 0475.28009