Abstract: In 2003 H. Bruin and S. Troubetzkoy studied a renormalization map for a
two-parameter family of interval translation maps. For a non-typical subset of the
parameter space the interval translation map has a Cantor attractor. The
renormalization G is a procedure similar to the Rauzy induction. It acts as dynamics
on the parameter space and can be used to find the attractor. In this talk we further
study these systems, focusing on weak mixing. We look at the symbolic representation
of the interval translation map to define a S-adic subshift and use results about the
eigenvalues of Bratteli-Vershik systems to determine whether the interval translation
map is weakly mixing. Additionally we characterize the subset of linearly recurrent
interval translation maps and their eigenvalues. This is joint work with Henk Bruin.
Interval Translation Maps with Weakly Mixing Attractors
22.09.2023 15:30 - 16:30
Organiser:
H. Bruin, R. Zweimüller
Location:
BME Budapest