In this talk I will discuss renormalization of low-dimensional dynamical systems and associated phenomena such as universality and rigidity.  The first part of the talk will be an introduction to the classical results in this field.  In the second part I will discuss new phenomena that appear in the article 'Instability of Renormalization' (arXiv:1609.04473).  In particular, I will introduce the renormalization operator acting on Lorenz maps (these are one-dimensional maps associated with three-dimensional flows undergoing a homoclinic bifurcation).  This operator turns out to have non-trivial dynamics inside topological classes of stationary type which in turns leads to the phenomena of coexistence and as dimensional discrepancy.  All of these notions will be explained in the talk.


Björn Winckler

Research Area



Imperial College London


Fri, 31/08/2018 - 4:00pm


RC-3085, The Red Centre, UNSW