Parry’s topological transitivity and $f$-expansions

Topological Transitivity and Strong Transitivity

We discuss the relation between (topological) transitivity and strong transitivity of dynamical systems. We show that a transitive and open self-map of a compact metric space satisfying a certain expanding condition is strongly transitive. We also prove a couple of results for interval maps; for example it is shown that a transitive piecewise monotone interval map is strongly transitive.

Topological transitivity

The concept of topological transitivity goes back to G. D. Birkhoff [1]

Random F-Expansions

Eta-expansions Iii | F !

The use of expansionary-rewrite rules in various typed-calculi has become increasingly common in recent years as their advantages over contractive-rewrite rules have become apparent. Not only does one obtain simultaneously a decision procedure for-equality and a procedure for the calculation of the long-normal form of a term, but rewrite relations using expansions retain key properties when com...

F - Expansions of rationals

The ergodic theorem has been used to deduce results about the F-expansions of almost all x in (0, 1)". A simple lemma from measure theory yields some corresponding statements about the expansions of the rationals, a set of measure zero.