I'm writting a short introductory report about chaos theory, and one of the conditions for a dynamical system to be chaotic seems to be the presence of topological mixing.
Now, the document I'm using as a guide hints that the presence of topological mixing is deeply entwined with a posive entropy of the system, but it does not state what partition of the space state it is using to define that entropy, or what is the (causal?) link between a positive entropy and the presence of topological mixing.
My questions, therefore, would be:
1.What partition is used in the definition of the entropy of a (general) dynamical system?
2.What relationship is there between topological mixing (or any other kind of mixing) and the entropy of a dynamical system?