# American Institute of Mathematical Sciences

November  2011, 30(4): 1237-1242. doi: 10.3934/dcds.2011.30.1237

## Zero entropy versus infinite entropy

 1 School of Mathematical Science, Peking University, Beijing 100871, China, China

Received  June 2010 Revised  December 2010 Published  May 2011

We construct a pair of equivalent flows with fixed points, such that one has infinite topological entropy and the other has zero topological entropy.
Citation: Wenxiang Sun, Cheng Zhang. Zero entropy versus infinite entropy. Discrete & Continuous Dynamical Systems - A, 2011, 30 (4) : 1237-1242. doi: 10.3934/dcds.2011.30.1237
##### References:
 [1] T. Ohno, A weak equivalence and topological entropy,, Publ. RIMS, 16 (1980), 289.  doi: 10.2977/prims/1195187508.  Google Scholar [2] W. Sun and E. Vargas, Entropy of flows, revisited,, Bol. Soc. Bra. Mat., 30 (1999), 313.  doi: 10.1007/BF01239009.  Google Scholar [3] W. Sun, T. Young and Y. Zhou, Topological entropies of equivalent smooth flows,, Trans. Amer. Math. Soc., 361 (2009), 3071.  doi: 10.1090/S0002-9947-08-04743-0.  Google Scholar [4] R. Thomas, Topological entropy of fixed-point free flows,, Trans. Amer. Math. Soc., 319 (1985), 601.  doi: 10.2307/2001256.  Google Scholar [5] P. Walters, "An Introduction to Ergodic Theory,", "An Introduction to Ergodic Theory,", (1982).   Google Scholar

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##### References:
 [1] T. Ohno, A weak equivalence and topological entropy,, Publ. RIMS, 16 (1980), 289.  doi: 10.2977/prims/1195187508.  Google Scholar [2] W. Sun and E. Vargas, Entropy of flows, revisited,, Bol. Soc. Bra. Mat., 30 (1999), 313.  doi: 10.1007/BF01239009.  Google Scholar [3] W. Sun, T. Young and Y. Zhou, Topological entropies of equivalent smooth flows,, Trans. Amer. Math. Soc., 361 (2009), 3071.  doi: 10.1090/S0002-9947-08-04743-0.  Google Scholar [4] R. Thomas, Topological entropy of fixed-point free flows,, Trans. Amer. Math. Soc., 319 (1985), 601.  doi: 10.2307/2001256.  Google Scholar [5] P. Walters, "An Introduction to Ergodic Theory,", "An Introduction to Ergodic Theory,", (1982).   Google Scholar
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