Transactions of the American Mathematical Society

Author(s): Wenxiang Sun; Todd Young; Yunhua Zhou
Journal: Trans. Amer. Math. Soc. 361 (2009), 3071-3082.
MSC (2000): Primary 37C15, 34C28, 37A10
Posted: December 29, 2008
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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.

1.: R. Bowen and P. Walters, Expansive one-parameter flows, J. Diff. Eq., 12 (1972), 180-193. MR 0341451 (49:6202)
2.: H. Furstenburg, Poincaré recurrence and number theory, Bull. A.M.S. 5 (1981), 211-234. MR 628658 (83d:10067)
3.: M.R. Herman, Construction d'un diffeomorphisme minimal d'entropie topologique non nulle, Erg. Th. Dyn. Systems, 1 (1981), 65-76. MR 627787 (83c:58046)
4.: A. Katok, Lyapunov exponents, entropy and periodic orbits for diffeomorphisms, Publ. IHES, 51 (1980), 137-173. MR 573822 (81i:28022)
5.: S.T. Liao, On the stability conjecture, Chinese Ann. Math. 1 (1980), no. 1, 9-30. MR 591229 (82c:58031)
6.: G. Maruyama, Theory of stationary processes and ergodic theory, A lecture at the Symposium held at Kyoto Univ., 1965.
7.: T. Ohno, A weak equivalence and topological entropy, Publ. RIMS, Kyoto Univ. 16 (1980), 289-298. MR 574037 (81g:54053)
8.: W. Sun and E. Vargas, Entropy of flows, revisited, Bol. Soc. Brasil. Mat. 30 (1999), 315-333. MR 1726916 (2001d:37007)
9.: W. Sun, Entropy of orthonormal -frame flows, Nonlinearity, 14 (2001), no. 4, 829-842. MR 1837641 (2002e:37032)
10.: R. Thomas, Topological entropy of fixed-point free flows, Trans. Amer. Math. Soc., 319 (1990), 601-618. MR 1010414 (90m:58178)
11.: R. Thomas, Entropy of expansive flows, Erg. Th. Dyn. Systems, 7 (1987), 611-625. MR 922368 (89a:54022)
12.: H. Totoki, Time changes of flows, Mem. Fac. Sci. Kyushu Univ., Ser. A, 20 (1966), 27-55. MR 0201606 (34:1488)
13.: P. Walters, An introduction to ergodic theory, Springer-Verlag, 1982. MR 648108 (84e:28017)

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 37C15, 34C28, 37A10

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: 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
Posted: 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).
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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