Speaker: Marta Maggioni (Universiteit Leiden, Netherlands)
Title: Matching for random systems with an application to minimal weight expansions
Abstract: We consider families of skew-product maps, representing
systems evolving in discrete time in which, at each time step, one of a
number of transformations is chosen according to an i.i.d process and
applied. We extend the notion of matching for such dynamical systems and
we show that, for a certain family of piecewise affine random maps of
the interval, the property of random matching implies that any invariant
density is piecewise constant. We give an application by introducing a
one-parameter family of random maps generating signed binary expansions
of numbers. This family has random matching for Lebesgue almost every
parameter, producing matching intervals that are related to the ones
obtained for the Nakada continued fraction transformations. We use this
property to study the expansions with minimal weight. Joint with K.
Dajani and C. Kalle.
Time and location:
Wed, 01 Jul 2020 17:00:00 UTC -
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