I am trying to investigate the expectation value of a quantum Hamiltonian where one of the parameters of the quantum evolution is a 1-D chaotic map. I don't have any formal training on dynamical systems. After reading couple of papers, my intuition is that the invariant measure of a chaotic map should be my starting point to self-teach the concept and eventually proceed to investigate the problem in hand. Now I am looking for a text/reference to study invariant measure of simple logistic/kent maps. Would it be reasonable to buy any or both of the following books? Or does anyone have any other suggestion?
- Lasota, Andrzej, and Michael C. Mackey. Chaos, fractals, and noise: stochastic aspects of dynamics. Vol. 97. Springer Science & Business Media, 2013.
- Boyarsky, Abraham, and Pawel Gora, eds. Laws of chaos: invariant measures and dynamical systems in one dimension. Springer Science & Business Media, 2012.
Thanks in advance.