Speaker: James A. Yorke (University of Maryland)
Time: 26/2 11:00 AM
Abstract: Yoshi Saiki (Tokyo) and I have been investigating examples of dynamical systems, i.e., maps, that are “heterogeneous”: they are ergodic and the system has different numbers of expanding directions in different regions of the space. In this talk I investigate a variant of this problem where we have a set of scalar affine maps of the form
tau_j(x) = a_j x + c_j for j = 1,…,N,
especially when N = 2, and especially when one map is expanding and another is contracting, i.e., a_1 > 1 > a_2 > 0.
A trajectory consists of a random (iid) sequence of the N maps, j_1, j_2, j_3, …. applied iteratively to some initial point x in R. The behaviors of such trajectories is surprising.
We have used extensive numerical simulations to guide our research to find what is likely to be true or important. The most valuable simulation is one that surprises. The title of this talk suggests what Yoshi and I can prove.
Location: Online
Zoom Meeting No.: 423 317 8953 (Passcode: SIMIS)
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