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A note on the relation between asymptotic rates of a flow under a function and its basis-automorphism. (English) Zbl 0699.28008

Let \((S_ t)_{t\in {\mathbb{R}}}\) denote a flow under the function f with base transformation S. Denote by \(L((S_ t))\) and L(S) the asymptotic rates of \((S_ t)\) and S, respectively [K. Winkelbauer, Commentat.Math. Univ. Carol. 18, 789-812 (1977; Zbl 0368.28020)]. The author proves that \[ ess \inf E(f| {\mathcal I})L((S_ t))\leq L(S)\leq ess \sup E(F| {\mathcal I})L(S_ t))\quad, \] where \({\mathcal I}\) denotes the \(\sigma\)-algebra of S-invariant sets.
Reviewer: M.Denker

MSC:

28D10 One-parameter continuous families of measure-preserving transformations
28D20 Entropy and other invariants

Citations:

Zbl 0368.28020
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