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Topological entropy on subsets for fixed-point free flows
Department of Mathematics, Nanjing University, Nanjing, Jiangsu 210093, China |
By considering all possible reparametrizations of the flows instead of the time-$1$ maps, we introduce Bowen topological entropy and local entropy on subsets for flows. Through handling techniques for reparametrization balls, we prove a covering lemma for fixed-point free flows and then prove a variational principle.
References:
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R. Bowen,
Entropy for group endomorphisms and homogeneous spaces, Trans. Amer. Math. Soc., 153 (1971), 401-414.
doi: 10.1090/S0002-9947-1971-0274707-X. |
| [2] |
R. Bowen,
Periodic orbits for hyperbolicf lows, Amer. J. Math., 94 (1972), 1-30.
doi: 10.2307/2373590. |
| [3] |
R. Bowen,
Topological entropy for noncompact sets, Trans. Amer. Math. Soc., 184 (1973), 125-136.
doi: 10.1090/S0002-9947-1973-0338317-X. |
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D. J. Feng and W. Huang,
Variational principles for topological entropies of subsets, J. Funct. Anal., 263 (2012), 2228-2254.
doi: 10.1016/j.jfa.2012.07.010. |
| [5] |
P. Mattila,
Geometry of Sets and Measures in Euclidean Spaces, Cambridge University Press, 1995.
doi: 10.1017/CBO9780511623813. |
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Ya. B. Pesin,
Dimension Theory in Dynamical Systems. Contemporary Views and Applications, University of Chicago Press, Chicago, IL, 1997.
doi: 10.7208/chicago/9780226662237.001.0001. |
| [7] |
W. X. Sun,
Measure-theoretic entropy for flows, Science in China Series A: Mathematics, 40 (1997), 725-731.
doi: 10.1007/BF02878695. |
| [8] |
W. X. Sun and E. Vargas,
Entropy of flows, revisited, Bol. Soc. Brasil. Mat. (N.S.), 30 (1999), 315-333.
doi: 10.1007/BF01239009. |
| [9] |
R. F. Thomas,
Entropy of expansive flows, Ergod. Th. Dynam. Sys., 7 (1987), 611-625.
doi: 10.1017/S0143385700004235. |
| [10] |
R. F. Thomas,
Topological entropy of fixed-point free flows, Trans. Amer. Math. Soc., 319 (1990), 601-618.
doi: 10.1090/S0002-9947-1990-1010414-5. |
show all references
References:
| [1] |
R. Bowen,
Entropy for group endomorphisms and homogeneous spaces, Trans. Amer. Math. Soc., 153 (1971), 401-414.
doi: 10.1090/S0002-9947-1971-0274707-X. |
| [2] |
R. Bowen,
Periodic orbits for hyperbolicf lows, Amer. J. Math., 94 (1972), 1-30.
doi: 10.2307/2373590. |
| [3] |
R. Bowen,
Topological entropy for noncompact sets, Trans. Amer. Math. Soc., 184 (1973), 125-136.
doi: 10.1090/S0002-9947-1973-0338317-X. |
| [4] |
D. J. Feng and W. Huang,
Variational principles for topological entropies of subsets, J. Funct. Anal., 263 (2012), 2228-2254.
doi: 10.1016/j.jfa.2012.07.010. |
| [5] |
P. Mattila,
Geometry of Sets and Measures in Euclidean Spaces, Cambridge University Press, 1995.
doi: 10.1017/CBO9780511623813. |
| [6] |
Ya. B. Pesin,
Dimension Theory in Dynamical Systems. Contemporary Views and Applications, University of Chicago Press, Chicago, IL, 1997.
doi: 10.7208/chicago/9780226662237.001.0001. |
| [7] |
W. X. Sun,
Measure-theoretic entropy for flows, Science in China Series A: Mathematics, 40 (1997), 725-731.
doi: 10.1007/BF02878695. |
| [8] |
W. X. Sun and E. Vargas,
Entropy of flows, revisited, Bol. Soc. Brasil. Mat. (N.S.), 30 (1999), 315-333.
doi: 10.1007/BF01239009. |
| [9] |
R. F. Thomas,
Entropy of expansive flows, Ergod. Th. Dynam. Sys., 7 (1987), 611-625.
doi: 10.1017/S0143385700004235. |
| [10] |
R. F. Thomas,
Topological entropy of fixed-point free flows, Trans. Amer. Math. Soc., 319 (1990), 601-618.
doi: 10.1090/S0002-9947-1990-1010414-5. |
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