Where can I find out more on Collatz-conjecture like sequences?

Question

I'm interested in Collatz-conjecture (the 3n+1 problem) like sequences. I'm interested in any literature that contains information about problems that are divided into similar cases.

I'm particularly interested in studies of sequences that have 3 or more cases, but information on 2 case problems is interesting as well.

I'm just trying to get a feel of what is known. Anything will be helpful.

So, where can we find lots of information on these types of problems/sequences?

Answer 1

Anyone wanting to study the $3n+1$ problem and related sequences should check Jeffrey Lagarias' annotated bibliographies on the arXiv, posted here and here. It contains some hundreds of papers, with for each paper a short summary of what it is about.

Answer 2

A natural generalization of the Collatz problem is recursively undecidable.

You may be interested in this paper.