Math Seminars
O. Butterley
(Imperial College)
Hyperbolic systems and functional analysis
I will give a brief overview of recent work in this area and what results have been produced. Additionally I will introduce the ideas by looking explicitly at expanding systems and demonstrate the components of the method: Carefully chosen norms, Lasota-Yorke style inequality, compact embedding of Banach spaces and a quasi compact spectrum and consequently statistical properties. Finally, for hyperbolic maps, I consider the choice of norms a la Gouezel- Liverani.