Abstract
We show that a flow or a semiflow with a weak form of reparametrized gluing orbit property has positive topological entropy if it is not minimal.
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References
Tian X Sun W. Diffeomorphisms with various C1-stable properties. Acta Mathematica Scientia, 2012, 32B(2): 552–558
Climenhaga V Thompson D. Unique equilibrium states for flows and homeomorphisms with non-uniform structure. Adv Math 2016, 303:744–799
Bomfim T Varandas P. The gluing orbit property, uniform hyperbolicity and large deviations principles for semiflows. Journal of Differential Equations 2019, 267(1):228–266
Bomfim T Torres M J Varandas P. Topological features of flows with the reparametrized gluing orbit property. Journal of Differential Equations 2017, 262(8):4292–4313
Bessa M Torres M J Varandas P. On the periodic orbits, shadowing and strong transitivity of continuous flows. Nonlinear Analysis 2018, 175:191–209
Shao X Yin Z. Multifractal analysis for maps with the gluing orbit property. Taiwanese Journal of Math- ematics 2017, 21:1099–1113
Tian X, Wang S Wang X. Intermediate Lyapunov exponents for system with periodic gluing orbit property. Discrete and Continuous Dynamical Systems - A 2019, 39(2):1019–1032
Constantine D Lafont J Thompson D. The weak specification property for geodesic flows on CAT(-1) spaces (to appear in Groups, Geometry, and Dynamics)
Sun P. Ergodic measures of intermediate entropies for dynamical systems with approximate product property. Preprint, 2019
Sun P. Minimality and gluing orbit property. Discrete and Continuous Dynamical Systems - A 2019, 39(7):4041–4056
Sun P. Zero-entropy dynamical systems with gluing orbit property. Preprint, 2019
Sun P. Unique ergodicity for zero-entropy dynamical systems with approximate product property. Preprint, 2019
Bowen R. Periodic points and measures for Axiom A diffeomorphisms. Trans Amer Math Soc 1971, 154:377–397
Denker M Grillenberger C Sigmund K. Ergodic theory on compact spaces. Lecture Notes in Mathematics. Vol. 527. Berlin-New York: Springer-Verlag, 1976
Kwietniak D Lacka M Oprocha P. A panorama of specification-like properties and their consequences. Contemporary Mathematics 2016, 669:155–186
Bowen R Ruelle D. The ergodic theory of Axiom A flows. Invent Math 1975, 29(3):181–202
Acknowledgements
The author would like to thank Paulo Varandas, Xueting Tian, and the anonymous referees for their helpful comments and suggestions.
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Peng Sun is supported by National Natural Science Foundation of China (11571387) and CUFE Young Elite Teacher Project (QYP1902).
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Sun, P. On the Entropy of Flows with Reparametrized Gluing Orbit Property. Acta Math Sci 40, 855–862 (2020). https://doi.org/10.1007/s10473-020-0318-z
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DOI: https://doi.org/10.1007/s10473-020-0318-z