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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Topological entropies of equivalent smooth flows


Authors: Wenxiang Sun, Todd Young and Yunhua Zhou
Journal: Trans. Amer. Math. Soc. 361 (2009), 3071-3082
MSC (2000): Primary 37C15, 34C28, 37A10
Published electronically: December 29, 2008
MathSciNet review: 2485418
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Abstract: We construct two equivalent smooth flows, one of which has positive topological entropy and the other has zero topological entropy. This provides a negative answer to a problem posed by Ohno.


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Additional Information

Wenxiang Sun
Affiliation: LMAM, School of Mathematical Sciences, Peking University, Beijing, People’s Republic of China
Email: sunwx@math.pku.edu.cn

Todd Young
Affiliation: Department of Mathematics, Ohio University, Athens, Ohio 45701
Email: young@math.ohiou.edu

Yunhua Zhou
Affiliation: School of Mathematical Sciences, Peking University, Beijing, People’s Republic of China
Email: zhouyh@math.pku.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04743-0
PII: S 0002-9947(08)04743-0
Keywords: Measure-theoretic entropy, equivalent flow, singularity.
Received by editor(s): May 31, 2007
Published electronically: December 29, 2008
Additional Notes: The first author was supported by NSFC (#10231020, #10671006) and National Basic Research Program of China (973 Program) (#2006CB805900).
The second author was supported by an Ohio University Faculty Fellowship Leave
The third author was supported by NSFC (#10671006).
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.