Abstract
AbstractWe give a necessary and sufficient condition on $\beta $ of the natural extension of a $\beta $ -shift, so that any equilibrium measure for a function of bounded total oscillations is a weak Gibbs measure.
Highlights
We study equilibrium measures of the natural extension of β-shifts
This is an interesting class of dynamical systems which have been studied in ergodic and number theory since the fundamental papers [Re, Pa]
We want to determinate whether an equilibrium measure for a continuous function φ is a weak Gibbs measure
Summary
We study equilibrium measures of the natural extension of β-shifts. This is an interesting class of dynamical systems which have been studied in ergodic and number theory since the fundamental papers [Re, Pa]. Let Pβ be the set of the prefixes of the sequence cβ , including the empty word ǫ. Let f ∈ C(AZ) be a continuous function defined on the full shift AZ.
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