Math Seminar: Analysis of P-recurrence: A Dynamical System Point of View

Monday, May 6, 2019

2:00 PM-3:00 PM

Thomas Yu, Drexel University

Abstract: D-finite functions, or the corresponding P-recurrences, encompass as special cases all hypergeometric functions and therefore can potentially appear in many applications involving special functions. (For instance, this happened to the speaker when he was analyzing a specific geometric configuration arising from biomembranes.) After reviewing the basic definition and properties, together with some simple examples, of D-finite functions and P-recurrences, a natural dynamical system associated with a P-recurrence will be presented. It is then shown that the system has a stable fixed point if and only if the dominant root of the characteristic polynomial of the recurrence is simple. The stability makes it easy to answer certain questions (e.g. positivity) about the recurrence. There are, however, interesting examples in which the dominant root is not simple. In this difficult case, a modification is proposed that stabilizes the dynamical system.

Contact Information

Hugo Woerdeman
hugo@math.drexel.edu