Event Type:

Number Theory Seminar

Date/Time:

Tuesday, November 7, 2017 - 16:00 to 17:15

Local Speaker:

Abstract:

Abstract: Having lingered on motivation last time, this week we add precision. In particular, we introduce a uniform Hausdorff metric on the space of those compact subsets of a complete metric space Y which fiber surjectively onto a compact metric space, I. Given an expansive map f of I, we construct a related contraction; when I \subset Y = R^n, the contraction's fixed point comes with a map F for which Lebesgue measure, m, is invariant. Under reasonable assumptions, the dynamical system defined by (F, m) is a `natural extension' for that defined by f with the (marginal) measure given by integrating along fibers.