Breadcrumb
Isomorphisms between certain piecewise linear maps
Thu 07 March 2013, 15:00
Charlene Kalle
Universiteit Leiden
Ergodic Theory and Dynamical Systems
Organisers: Andrew Ferguson, Thomas Jordan
ABSTRACT
The $\beta$-transformation is a piecewise linear interval map with
constant slope $\beta>1$. It is a very well studied map. It can be used
to dynamically generate number expansions with non-integer base of
numbers in the unit interval, called $\beta$-expansions. In recent years
there has been some interest in so-called negative $\beta$-expansions.
These are number expansions in base $-\beta$. Many of the combinatorial
properties of these expansions coincide. Since there also exists a
dynamical system that generates the negative expansions by iteration,
the question of how similar the two underlying dynamical systems are
naturally arises. In dynamical terms, we are looking for an isomorphism
between two interval maps that cannot be modelled by a finite alphabet
Markov chain.