Collision resistant Hash function in chaos cryptography
Chaos-based encryption ain't an active area of research among the best crypto researchers; it's looking like a dead end.  You might find papers published on the topic, but they're generally in lower-reputation conferences.  Why is it a dead end?  Because it doesn't seem to work.  The schemes typically end up being either insecure, or worse than existing algorithms (e.g., slower).  Basically, it initially sounded like an intriguing idea, but at this point I would advise you that studying chaos-based cryptography appears to be a waste of your time, if you want to accomplish something useful or practical.  (See also https://security.stackexchange.com/q/31000/971, though it doesn't really address this point.)

You can't prove collision-resistance.  Even the state-of-the-art hash functions don't come with a mathematical proof of collision-resistance.  See https://crypto.stackexchange.com/q/18730/351 and https://crypto.stackexchange.com/q/26094/351 and https://security.stackexchange.com/q/5101/971.