I'm working with dynamical systems defined by ODEs and SDEs, in this latter case gradient systems in particular, a special case of Ito diffusions.
I've read that under reasonable assumptions this gradient systems are geometrically ergodic, but I'm new to the field of Ergodic theory. Does geometric ergodicity mean ergodic system with some kind of "exponential convergence"?
Could you recommend a book/review paper/notes where ergodicity is introduced in the context of Hamiltonian systems and stochastic differential equations (such as Ito diffusions)?
