# On continuous actions commutingwith actions of positive entropy

Colloquium Mathematicae (1996)

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

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topShereshevsky, 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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- [W] P. Walters, An Introduction to Ergodic Theory, Springer, New York, 1982. Zbl0475.28009

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