Laplace transforms of polynomially bounded vector-valued functions and semigroups of operators |
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Authors: | R DeLaubenfels Z Huang S Wang Y Wang |
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Institution: | (1) Institut de Mathématiques de Luminy, CNRS - UPR 9016 Case 930, 163 avenue de Luminy, F13288 Marseille Cedex 9, France |
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Abstract: | We define an invariant of measure-theoretic isomorphism for dynamical systems, as the growth rate inn of the number of small
-balls aroundα-n-names necessary to cover most of the system, for any generating partitionα. We show that this rate is essentially bounded if and only if the system is a translation of a compact group, and compute
it for several classes of systems of entropy zero, thus getting examples of growth rates inO(n),O(n
k
) fork ε ℕ, oro(f(n)) for any given unboundedf, and of various relationships with the usual notion of language complexity of the underlying topological system. |
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Keywords: | |
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