I think there are several papers that can give you a good introduction. The seminal papers of Parry and Rényi have been already mentioned as well as Dajani-Kraikaamp's book. I think that Nikita Sidorov's paper Arithmethic Dynamics is very useful as well as his lecture notes. Also Dajani&Kraaikamp's paper From Greedy to Lazy expansions and their driving dynamics is relevant as well as Komornik's paper Expansions in noninteger bases.

Now, Simon Baker's and Derong Kong's papers contain very well written brief introductions to the topic.

I think there are several papers that can give you a good introduction. The seminal papers of Parry and Rényi have been already mentioned as well as Dajani-Kraikaamp's book. I think that Nikita Sidorov's paper Arithmethic Dynamics is very useful as well as his lecture notes. Also Dajani&Kraaikamp's paper From Greedy to Lazy expansions and their driving dynamics is relevant as well as Komornik's paper Expansions in noninteger bases.

Now, Simon Baker's and Derong Kong's papers contain very well written brief introductions to the topic.

EDIT I found these notes today. http://wisdyn.math.uni-bremen.de/betabremen.pdf http://wisdyn.math.uni-bremen.de/Lingmin.pdf