Title: Topological Dynamics of Piecewise Lambda-Affine Maps

Abstract: Lambda-affine maps are functions on a closed interval which are piecewise, with the pieces defined by a set of parallel lines. Though this seems very specific, such maps are conjugate or semi-conjugate to many other piecewise smooth maps. We wish to explore the long-term behavior of such functions over repeated iterations. Using Iterated Function Systems, we deduce that (Lebesgue) almost every vertical shift of such an affine map is asymptotically periodic. More precisely, given a piecewise lambda-affine map made defined on n disjoint intervals, repeated composition of a function f + delta (mod 1) will converge to exactly 2n periodic orbits.

About the Speaker: Rob joined the pure math graduate program at UNM in Fall 2018.

Zoom Meeting ID: 937 6606 4787