Abstract:While an extreme growth rate of periodic orbits is an invariant for equivalent flows without fixed points, there exists a pair of equivalent flows with fixed points such that the growth rate of periodic orbits of one flow is infinite and that of the other is zero.
- Rufus Bowen, Periodic orbits for hyperbolic flows, Amer. J. Math. 94 (1972), 1–30. MR 298700, DOI 10.2307/2373590
- Taijiro Ohno, A weak equivalence and topological entropy, Publ. Res. Inst. Math. Sci. 16 (1980), no. 1, 289–298. MR 574037, DOI 10.2977/prims/1195187508
- V. A. Rohlin, Entropy of metric automorphism, Dokl. Akad. Nauk SSSR 124 (1959), 980–983 (Russian). MR 0103258
- Wenxiang Sun and Edson Vargas, Entropy of flows, revisited, Bol. Soc. Brasil. Mat. (N.S.) 30 (1999), no. 3, 315–333. MR 1726916, DOI 10.1007/BF01239009
- W. Sun and C. Zhang, Zero topological entropy versus infinite topological entropy, Dis. Con. Dyn. Sys. 30 (2011), 1237-1242.
- Peter Walters, An introduction to ergodic theory, Graduate Texts in Mathematics, vol. 79, Springer-Verlag, New York-Berlin, 1982. MR 648108
- Wenxiang Sun
- Affiliation: LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China
- MR Author ID: 315192
- Email: email@example.com
- Cheng Zhang
- Affiliation: School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China
- Email: firstname.lastname@example.org
- Received by editor(s): August 18, 2010
- Received by editor(s) in revised form: January 5, 2011
- Published electronically: August 5, 2011
- Additional Notes: The first author was supported by NSFC (#10831003) and the National Basic Research Program of China (973 Program) (#2006CB805903) and the National Education Ministry of China.
- Communicated by: Yingfei Yi
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
- Journal: Proc. Amer. Math. Soc. 140 (2012), 1387-1392
- MSC (2010): Primary 37C15, 34C28, 37A10
- DOI: https://doi.org/10.1090/S0002-9939-2011-10997-3
- MathSciNet review: 2869122