Mixing properties for nonautonomous linear dynamics and invariant sets

We study mixing properties (topological mixing and weak mixing of arbitrary order) for nonautonomous linear dynamical systems that are induced by the corresponding dynamics on certain invariant sets. The kinds of nonautonomous systems considered here can be defined using a sequence of linear operators on a topological vector space X such that there is an invariant set Y for which the dynamics restricted to Y satisfies a certain mixing property. We then obtain the corresponding mixing property on the closed linear span of Y. We also prove that the class of nonautonomous linear dynamical systems that are weakly mixing of order nn contains strictly the corresponding class with the weak mixing property of order n+1.This work was supported in part by MEC and FEDER, Project MTM2010-14909, and by GV, Project PROMETEO/2008/101. The first author was also supported by a grant from the FPU Program of MEC. We thank the referees whose reports led to an improvement in the presentation of this work.Murillo Arcila, M.; Peris Manguillot, A. (2013). Mixing properties for nonautonomous linear dynamics and invariant sets. Applied Mathematics Letters. 26(2):215-218. https://doi.org/10.1016/j.aml.2012.08.014S21521826

Entropy of nonautonomous dynamical systems

Different notions of entropy play a fundamental role in the classical theory of dynamical systems. Unlike many other concepts used to analyze autonomous dynamics, both measure-theoretic and topological entropy can be extended quite naturally to discrete-time nonautonomous dynamical systems given in the process formulation. This paper provides an overview of the author's work on this subject. Also an example is presented that has not appeared before in the literature