Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-28T20:04:37.112Z Has data issue: false hasContentIssue false
  • English
  • Français

Minimal F2-flows

Part of: Connections with other structures, applications Locally compact groups and their algebras

Published online by Cambridge University Press:  09 April 2009

Daniel Berend
Daniel Berend
Affiliation:
Department of MathematicsUniversity of California Los Angeles, California 90024, U.S.A.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let σ be an ergodic endomorphism of the r–dimensional torus and Π a semigroup generated by two affine transformations lying above σ. We show that the flow defined by Π admits minimal sets of positive Hausdorff dimension and we give necessary and sufficient conditions for this flow to be minimal.

MSC classification

Secondary: 22D40: Ergodic theory on groups 54H20: Topological dynamics
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 39 , Issue 2 , October 1985 , pp. 187 - 193
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Berend, D., “Multi-invariant sets on tori,” Trans. Amer. Math. Soc. 280 (1983), 509–532.CrossRefGoogle Scholar
[2]Berend, D., “Ergodic semigroups of epimorphisms,” to appear in Trans. Amer. Math. Soc.Google Scholar
[3]Furstenberg, H., “Disjointness in ergodic theory, minimal sets and a problem in diophantine approximations,” Math. Systems Theory 1 (1967), 1–49.CrossRefGoogle Scholar
[4]Keynes, H. B. and Sears, M., “Real-expansive flows and topological dimension,” Ergodic Theory Dynamical Systems 1 (1981), 179–195.CrossRefGoogle Scholar
[5]Mañé, R., “Expansive homemorphisms and topological dimension,” Trans. Amer. Math. Soc. 252 (1979), 313–319.CrossRefGoogle Scholar
[6]Pisot, C., “La répartition modulo 1 et le nombres algébriques,” Annali di Pisa (2) 7 (1938), 205–248.Google Scholar