Auslander systems
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- by Kamel N. Haddad and Aimee S. A. Johnson PDF
- Proc. Amer. Math. Soc. 125 (1997), 2161-2170 Request permission
Abstract:
The authors generalize the dynamical system constructed by J. Auslander in 1959, resulting in perhaps the simplest family of examples of minimal but not strictly ergodic systems. A characterization of unique ergodicity and mean-L-stability is given. The new systems are also shown to have zero topological entropy and fail to be weakly rigid. Some results on the set of idempotents in the enveloping semigroup are also achieved.References
- Joseph Auslander, Mean-$L$-stable systems, Illinois J. Math. 3 (1959), 566–579. MR 149462
- J. Auslander and K. Berg, A condition for zero entropy, Israel J. Math. 69 (1990), no. 1, 59–64. MR 1046173, DOI 10.1007/BF02764729
- Robert Ellis, Lectures on topological dynamics, W. A. Benjamin, Inc., New York, 1969. MR 0267561
- Morgan Ward and R. P. Dilworth, The lattice theory of ova, Ann. of Math. (2) 40 (1939), 600–608. MR 11, DOI 10.2307/1968944
- S. Glasner and D. Maon, Rigidity in topological dynamics, Ergodic Theory Dynam. Systems 9 (1989), no. 2, 309–320. MR 1007412, DOI 10.1017/S0143385700004983
Additional Information
- Kamel N. Haddad
- Affiliation: Department of Mathematics, California State University at Bakersfield, Bakersfield, California 93311
- Email: khaddad@ultrix6.cs.csubak.edu
- Aimee S. A. Johnson
- Affiliation: Department of Mathematics & Statistics, Swarthmore College, Swarthmore, Pennsylvania 19081
- Email: aimee@swarthmore.edu
- Received by editor(s): August 15, 1995
- Received by editor(s) in revised form: January 16, 1996
- Communicated by: Mary Rees
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 2161-2170
- MSC (1991): Primary 54H20, 54H15
- DOI: https://doi.org/10.1090/S0002-9939-97-03768-4
- MathSciNet review: 1372033