  Most of the text algorithms build data structures on words, mainly trees, as
digital trees (tries) or binary search trees (bst). The mechanism which
produces symbols of the words (one symbol at each unit time) is called a
source, in information theory contexts. The probabilistic behaviour of the
trees built on words emitted by the same source depends on two factors: the
algorithmic properties of the tree, together with the information-theoretic
properties of the source. Very often, these two factors are considered in a too
simplified way: from the algorithmic point of view, the cost of the Bst is only
measured in terms of the number of comparisons between words --from the
information theoretic point of view, only simple sources (memoryless sources or
Markov chains) are studied.
  We wish to perform here a realistic analysis, and we choose to deal together
with a general source and a realistic cost for data structures: we take into
account comparisons between symbols, and we consider a general model of source,
related to a dynamical system, which is called a dynamical source. Our methods
are close to analytic combinatorics, and our main object of interest is the
generating function of the source Lambda(s), which is here of Dirichlet type.
Such an object transforms probabilistic properties of the source into analytic
properties. The tameness of the source, which is defined through analytic
properties of Lambda(s), appears to be central in the analysis, and is
precisely studied for the class of dynamical sources. We focus here on
arithmetical conditions, of diophantine type, which are sufficient to imply
tameness on a domain with hyperbolic shape.
