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.
Peng SUN
. ON THE ENTROPY OF FLOWS WITH REPARAMETRIZED GLUING ORBIT PROPERTY[J]. Acta mathematica scientia, Series B, 2020
, 40(3)
: 855
-862
.
DOI: 10.1007/s10473-020-0318-z
[1] Tian X, Sun W. Diffeomorphisms with various C1-stable properties. Acta Mathematica Scientia, 2012, 32B(2):552-558
[2] Climenhaga V, Thompson D. Unique equilibrium states for flows and homeomorphisms with non-uniform structure. Adv Math, 2016, 303:744-799
[3] 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
[4] 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
[5] Bessa M, Torres M J, Varandas P. On the periodic orbits, shadowing and strong transitivity of continuous flows. Nonlinear Analysis, 2018, 175:191-209
[6] Shao X, Yin Z. Multifractal analysis for maps with the gluing orbit property. Taiwanese Journal of Mathematics, 2017, 21:1099-1113
[7] 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
[8] Constantine D, Lafont J, Thompson D. The weak specification property for geodesic flows on CAT(-1) spaces (to appear in Groups, Geometry, and Dynamics)
[9] Sun P. Ergodic measures of intermediate entropies for dynamical systems with approximate product property. Preprint, 2019
[10] Sun P. Minimality and gluing orbit property. Discrete and Continuous Dynamical Systems-A, 2019, 39(7):4041-4056
[11] Sun P. Zero-entropy dynamical systems with gluing orbit property. Preprint, 2019
[12] Sun P. Unique ergodicity for zero-entropy dynamical systems with approximate product property. Preprint, 2019
[13] Bowen R. Periodic points and measures for Axiom A diffeomorphisms. Trans Amer Math Soc, 1971, 154:377-397
[14] Denker M, Grillenberger C, Sigmund K. Ergodic theory on compact spaces. Lecture Notes in Mathematics. Vol. 527. Berlin-New York:Springer-Verlag, 1976
[15] Kwietniak D, Lacka M, Oprocha P. A panorama of specification-like properties and their consequences. Contemporary Mathematics, 2016, 669:155-186
[16] Bowen R, Ruelle D. The ergodic theory of Axiom A flows. Invent Math, 1975, 29(3):181-202