Dynamical sources in information theory: Fundamental intervals and word prefixes (vol 29, pg 262, 2001)
In [V] the third author studied statistical properties of words generated by dynamical sources by using generalized Ruelle operators. This erratum aims to show that a supplementary condition should be added in Definition 2.1 of dynamical sources. This supplementary condition (called (d4) below) is closely related to the so-called Bounded Distortion Property and should be used at two different stages of the paper: first in the definition of the generalized operator G(s) second in the proof of Proposition 2 that deals with the Positivity Theorem of Krasnoselskii. We also prove that this condition is actually necessary and provide an example of a source which does not satisfy condition (d4) and for which G(s) is not well-defined.
information theory dynamical systems transfer operator dominant eigenvalues