Zero entropy factors of topological flows

Authors:
F. Blanchard and Y. Lacroix

Journal:
Proc. Amer. Math. Soc. **119** (1993), 985-992

MSC:
Primary 54H20; Secondary 28D20

DOI:
https://doi.org/10.1090/S0002-9939-1993-1155593-2

MathSciNet review:
1155593

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Abstract: The maximal zero entropy factor of a topological flow is defined using entropy pairs and explicitly given for some simple cartesian products. As a consequence, it is proved that only the trivial flow is disjoint from all flows whose maximal zero entropy factor is trivial.

**[AKM]**R. L. Adler, A. G. Konheim, and M. H. McAndrew,*Topological entropy*, Trans. Amer. Math. Soc.**114**(1965), 309-319. MR**0175106 (30:5291)****[Bl1]**F. Blanchard,*Full positive topological entropy and topological mixing*, Symbolic Dynamics and Applications (in honor of R. L. Adler), Contemp. Math., Amer. Math. Soc., Providence, RI (to appear). MR**1185082 (93k:58134)****[Bl2]**-,*A disjointness theorem involving topological entropy*, preprint, 1991.**[EG]**R. Ellis and W. H. Gottschalk,*Homomorphisms of transformation groups*, Trans. Amer. Math. Soc.**94**(1960), 258-271. MR**0123635 (23:A960)****[F]**H. Furstenberg,*Disjointness in ergodic theory, minimal sets, and a problem in diophantine approximation*, Math. Systems Theory**1**(1967), 1-49. MR**0213508 (35:4369)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1993-1155593-2

Keywords:
Topological entropy,
maximal zero entropy factor,
disjointness

Article copyright:
© Copyright 1993
American Mathematical Society