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

Zero entropy versus infinite entropy

Wenxiang Sun 1, and  Cheng Zhang 1,

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.
Keywords: Topological entropy, Equivalent flows..
Mathematics Subject Classification: 37C15, 34C28, 37A1.
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:
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T. Ohno, A weak equivalence and topological entropy,, Publ. RIMS, 16 (1980), 289. doi: 10.2977/prims/1195187508. Google Scholar

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W. Sun and E. Vargas, Entropy of flows, revisited,, Bol. Soc. Bra. Mat., 30 (1999), 313. doi: 10.1007/BF01239009. Google Scholar

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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

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R. Thomas, Topological entropy of fixed-point free flows,, Trans. Amer. Math. Soc., 319 (1985), 601. doi: 10.2307/2001256. Google Scholar

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P. Walters, "An Introduction to Ergodic Theory,", "An Introduction to Ergodic Theory,", (1982). Google Scholar

show all references

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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