Statistical Properties of Dynamical Systems by Quasicompactness of the Frobenius-Perron operator

Abstract: 

The chaotic behaviour of many dynamical systems leads to a strong analogy between trajectories and sequences of iid random variables. This leads to a Law of Large Numbers and Central Limit Theorem (CLT) for dynamical systems. The exact nature of these statistical laws is determined by the invariant measures of the dynamical system, which correspond to fixed points of the Frobenius-Perron operator. The property of quasicompactness is used to prove the existence of such a fixed point, and then to derive a CLT.