Event Type:

Number Theory Seminar

Date/Time:

Tuesday, November 1, 2016 - 16:00

Location:

BAT 250

Local Speaker:

Abstract:

As a follow up to my colloquium talk of last week, I’ll describe joint work with K. Allen and D. DeMark on the dynamics of Henon maps over non-Archimedean fields of odd residue characteristic. Depending on their coefficients, every such map exhibits exactly one of the following types of behavior: (i) good reduction, (ii) an attractor, (iii) a repeller, (iv) topological conjugacy to a two-sided shift map, or (v) no bounded orbits. In some cases the attractors/repellers can be infinite sets, but it is still an open problem to explain exactly when this situation occurs. We give an example in which the attractor is infinite, with dense forward orbits, and supporting an SRB-type measure describing the distribution of the forward orbit of any point in the basin of attraction.