## Dynamical Systems Seminars Spring 2017

The Dynamical Systems seminar is held on Monday afternoons at 4:00 PM in MCS 148. Tea beforehand is at 3:45 PM in MCS 144.

• January 23: Mike Todd (St Andrews)
Title: Stability of measures in interval dynamics
Abstract: Given a family of interval maps, each map possessing a `physical' measure (an invariant measure absolutely continuous w.r.t. Lebesgue), we have a weak form of stability if these measures change continuously through the family. Even for uniformly hyperbolic dynamical systems this stability can fail. I†¢ll give minimal conditions for a class of non-uniformly hyperbolic interval maps to satisfy this stability property. This work forms part of a paper with Neil Dobbs, where more general thermodynamic properties are proved to be stable (entropy, pressure, equilibrium states), and I†¢ll give some indication of the general approach there.

• January 30: Eric Chang (BU)
Title: The Sierpinski Mandelbrot spiral for the rational map
Abstract: We investigate the parameter plane for the family of maps $$F(z) = z^n + \lambda/z^d$$ where $$n \geq 4$$ is even, $$d \geq 3$$ is odd, and $$\lambda$$ is a complex parameter. Concentrating on $$F(z) = z^4 + \lambda / z^3$$, we prove the existence of two structures in the parameter plane: a Sierpinski Mandelbrot arc consisting of infinitely many alternating Sierpinski holes and Mandelbrot sets, as well as a Sierpinski Mandelbrot spiral consisting of infinitely many SM arcs. We also show that there are infinitely many SM spirals in the parameter plane.

• February 6: Osman Chaudhary (BU)
Title: TBA
Abstract: TBA

• February 13: No seminar planned; please consider attending the workshop at ICERM on The Dynamics of Small Scale Fluids.

• February 20: Holiday, No Seminar

• February 27: Alanna Hoyer-Leitzel (Mount Holyoke)
Title: TBA
Abstract: TBA

• March 6: Spring Break, No Seminar

• March 13: TBA
Title: TBA
Abstract: TBA

• March 20: No seminar planned; please consider attending the workshop at ICERM on Making a Splash - Droplets, Jets and Other Singularities.

• March 27: Patrick Cummings (BU)
Title: TBA
Abstract: TBA

• April 3: Noé Cuneo (McGill)
Title: TBA
Abstract: TBA

• April 10: Darko Volkov (WPI)
Title: TBA
Abstract: TBA

• April 17: Holiday, No Seminar

• April 24: No seminar planned; please consider attending the workshop at ICERM on Water Waves.

• May 1: Maxim Olshanii (UMass Boston)
Title: The Inverse Linearization Problem
Abstract: We investigate the relationship between the nonlinear partial differential equations (PDEs) of mathematical physics and the their linearizations around localized stationary solutions. It turns out that for some classes of PDEs, it is possible to solve the Inverse Linearization Problem, i.e. given the linearization, to restore the original PDE. Of a particular interest are the instances of transparency of the former that are shown to hint on the possible integrability of the latter.