References on Information Conservation and Hamiltonian Mechanics for Undergraduate Presentation

Question

As an undergraduate physics student, I am currently working on a presentation focused on applications of Hamiltonian mechanics. Specifically, I am interested in exploring the relationship between information conservation and Hamiltonian mechanics. I was wondering if anyone could recommend any references or resources that specifically discuss or prioritize this connection. I would greatly appreciate any suggestions or insights that could help enhance my understanding of this topic.