Cantor Sets, Bernoulli Shifts and Linear Dynamics
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Our purpose is to review some recent results on the interplay between the symbolic dynamics on Cantor sets and linear dynamics. More precisely, we will give some methods that allow the existence of strong mixing measures invariant for certain operators on Fréchet spaces, which are based on Bernoulli shifts on Cantor spaces. Also, concerning topological dynamics, we will show some consequences for the specification properties.
KeywordsHypercyclic operators Specification properties Strong mixing measures Weighted shifts
This work is supported in part by MICINN and FEDER, Projects MTM2010-14909 and MTM2013-47093-P. The third author is supported by a grant from the FPU Program of MEC. The second and fourth authors were partially supported by GVA, Project PROMETEOII/2013/013.
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