ENTROPY OF NONAUTONOMOUS DYNAMICAL SYSTEMS

• Zhu, Yujun ;
• Liu, Zhaofeng ;
• Xu, Xueli ;
• Zhang, Wenda
• Published : 2012.01.01
• 64 13

Abstract

In this paper, the topological entropy and measure-theoretic entropy for nonautonomous dynamical systems are studied. Some properties of these entropies are given and the relation between them is discussed. Moreover, the bounds of them for several particular nonautonomous systems, such as affine transformations on metrizable groups (especially on the torus) and smooth maps on Riemannian manifolds, are obtained.

Keywords

nonautonomous dynamical system;random dynamical system;topological entropy;measure-theoretic entropy

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3. Quasistatic dynamical systems 2016, https://doi.org/10.1017/etds.2016.9
4. Directional entropy of ℤ+k-actions vol.16, pp.01, 2016, https://doi.org/10.1142/S0219493716500040
5. Topological pressure for nonautonomous systems vol.76, 2015, https://doi.org/10.1016/j.chaos.2015.03.010
6. Estimations of topological entropy for non-autonomous discrete systems vol.22, pp.3, 2016, https://doi.org/10.1080/10236198.2015.1107055
7. Variational Principles for Entropies of Nonautonomous Dynamical Systems 2017, https://doi.org/10.1007/s10884-017-9586-2
8. On the topological entropy of free semigroup actions vol.435, pp.2, 2016, https://doi.org/10.1016/j.jmaa.2015.11.038
9. Metric Entropy of Nonautonomous Dynamical Systems vol.1, pp.1, 2014, https://doi.org/10.2478/msds-2013-0003
10. Topological and Measure-Theoretical Entropies of Nonautonomous Dynamical Systems 2016, https://doi.org/10.1007/s10884-016-9554-2
11. Relationships among some chaotic properties of non-autonomous discrete dynamical systems vol.24, pp.7, 2018, https://doi.org/10.1080/10236198.2018.1458101

Acknowledgement

Supported by : National Natural Science Foundation of China