Events

We study continuity properties of dynamical quantities while crossing the Mandelbrot set through typical smooth curves. In particular, we prove that for almost every parameter c₀ in the boundary of the Mandelbrot set M with respect of the harmonic measure and every smooth curve γ:[−1,1]→ C with the property that c₀=γ(0) there exists a set A_γ having 0 as a Lebesgue density point and such that that lim_{x→ 0} HDim(J_γ(x) = HDim(J_c0) for the Julia sets J_c. (joint work with Jacek Graczyk)

MAGIC Launch Lecture: Chaos, numbers and fractuals: the MAGIC of ergodic theory
Charles Walkden (University of Manchester)
Abstract: Dynamical systems is the study of iteration: given a map T acting on a space X and a point x ∈ X, what happens when one repeatedly applies the map T to x? Often, dynamical systems are chaotic: two points x,y ∈ X that start very close to each other can have very different behaviours under iteration. Instead of trying to understand the behaviour of every point under iteration, ergodic theory takes a more qualitative view: what does the long-term behaviour of a typical point look like? In addition, subsets of X that are invariant under the dynamics have a complicated structure and are commonly `fractal' in nature. We will see how these notions fit together and allow us to obtain some striking and surprising results in number theory.

I will be demonstrating MAGIC and the Visimeet Video Conferencing software for Node Representatives and Lecturers on Wed 30 Sep 2015 at 3pm. I strongly recommend that you attend even if you are comfortable using the software as there have been some changes since last semester.