Minimal Periodic Orbit Structure of 2-DimensionalHomeomorphisms

We present a method for estimating the minimal periodic orbit structure,the topological entropy, and a fat representative of the homeomorphismassociated with the existence of a finite collection of periodic orbits ofan orientation-preserving homeomorphism of the disk D². The method focuses on the concept of fold and recurrent bogustransition and is more direct than existing techniques. In particular,we introduce the notion of complexity to monitor the modification process used to obtain the desired goals. An algorithm implementing the procedure is described and some examples are presented at the end.