62,019 research outputs found
On finite limit sets for transformations on the unit interval
AbstractAn infinite sequence of finite or denumerable limit sets is found for a class of many-to-one transformations of the unit interval into itself. Examples of four different types are studied in some detail; tables of numerical results are included. The limit sets are characterized by certain patterns; an algorithm for their generation is described and established. The structure and order of occurrence of these patterns is universal for the class
On embedding of the Bratteli diagram into a surface
We study C*-algebras O_{\lambda} which arise in dynamics of the interval
exchange transformations and measured foliations on compact surfaces. Using
Koebe-Morse coding of geodesic lines, we establish a bijection between Bratteli
diagrams of such algebras and measured foliations. This approach allows us to
apply K-theory of operator algebras to prove strict ergodicity criterion and
Keane's conjecture for the interval exchange transformations.Comment: final versio
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