I've recently started taking a discrete-time dynamical systems perspective on a topic. I've been able to introduce a reasonable metric on a set, obtaining a compact space. Under that metric, a nice class of functions are continuous.
I'm now searching for theory that will allow me to get a better understanding of the behaviour of the class functions.
Can you recommend sources / lists of results that apply to continuous maps on compact spaces?
I know of Conley's Decomposition Theorem and am looking for similar, including both more basic and advanced. As this is not my area of expertise, any references would be appreciated.