Jason Bell, U Waterloo
12:00 PM - 1:00 PM
Given a complex variety and a rational self-map , one of the most important quantities in understanding the corresponding dynamical system is the dynamical degree, which is a nonnegative real number that gives some measure of how complex the system is. The dynamical degree is often a nonnegative integer and in many settings has been proved to be an algebraic number, including the case of endomorphisms of the plane. This naturally leads to the question: can the dynamical be transcendental? We show that the answer to this question is `yes’, by giving a rational self-map of the projective plane and using techniques from Diophantine approximation to exhibit the transcendence of the dynamical degree .
This is joint work with Jeff Diller and Mattias Jonsson.
Event contact: dinesh dot thakur at rochester dot edu