Minimal Periodic Orbit Structure of 2--Dimensional Homeomorphisms

HERNAN GUSTAVO SOLARI; NATIELLO, MA

Journal of Nonlinear Science

Springer

Año: 2005 vol. 15 p. 183 - 222

0938-8974

Summary. We present a method for estimating the minimal periodic orbit structure, the topological entropy, and a fat representative of the homeomorphism associated with the existence of a finite collection of periodic orbits of an orientation-preserving homeomorphism of the disk D2. The method focuses on the concept of fold and recurrent bogus transition 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. Keywords. 2-D homeomorphisms of the disk, Thurston classification theorem, minimal periodic orbit structure, topological entropy, pseudo-Anosov representative