The shape of an attractor
John Hunton (University of Leicester)
Monday 28th November, 2011 16:00-17:00 204
Suppose we have a compact differentiable manifold M with a diffeomorphism d:M --> M defining a hyperbolic dynamical system, so at each point the tangent space splits into a direct sum of expanding and contracting directions for the derivative of the map d. Suppose A is an attractor for this system (roughly, a connected limit set of points reached by iterating the action of d). What can A look like, even through the eyes of basic topological invariants, cohomology, K-theory etc? Generally A can be very complicated indeed, but we shall look at the case of those attractors of dimension one less than that of M, and show that there is a remarkable connection between each such attractor and moduli spaces of aperiodic tilings, objects for which there is already powerful machinery available for analysis. The talk will make no assumptions of knowledge of dynamical systems, attractors, aperiodic tilings or their moduli spaces which will all be suitably introduced.