The most accessible introduction (in my opinion) is 'Laws of Chaos - Invariant Measures and Dynamical Systems in One Dimension' by Boyarsky and Gora. For a shor

The most accessible introduction (in my opinion) is 'Laws of Chaos - Invariant Measures and Dynamical Systems in One Dimension' by Boyarsky and Gora. For a short survey on just stability of the invariant measure you could look at 'Linear Response, Or Else' by Baladi. I also like the lecture notes 'Statistical properties of uniformly hyperbolic maps and transfer operators' spectrum' by Carlangelo Liverani.