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Auslander systems
Author(s):
Kamel
N.
Haddad;
Aimee
S. A.
Johnson
Journal:
Proc. Amer. Math. Soc.
125
(1997),
2161-2170.
MSC (1991):
Primary 54H20, 54H15
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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:
- 1.
- J. Auslander, Mean-L-stable systems, Illinois Journal of Math., 1959, pp. 566-579. MR 26:6950
- 2.
- J. Auslander and K. Berg, A condition for zero entropy , Israel J. of Math.,vol. 69, 1990, pp. 59-64. MR 91d:54045
- 3.
- R. Ellis, Lectures on Topological Dynamics , W. A. Benjamin, 1969. MR 42:2463
- 4.
- E.E. Floyd, A non-homogeneous minimal set , Bull. Amer. Math. Soc.,vol. 55, 1949, pp. 957-960 MR 11:453g
- 5.
- S.Glasner and D.Maon, Rigidity in topological dynamics , Ergodic Theory and Dynamical Systems,vol. 9, 1989 MR 90h:54050
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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
DOI:
10.1090/S0002-9939-97-03768-4
PII:
S 0002-9939(97)03768-4
Keywords:
Dynamical system,
minimality,
proximality,
entropy,
unique ergodicity,
enveloping semigroup
Received by editor(s):
August 15, 1995
Received by editor(s) in revised form:
January 16, 1996
Communicated by:
Mary Rees
Copyright of article:
Copyright
1997,
American Mathematical Society
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