Numbering homoclinic points of diffeomorphisms in the plane (Q1199843)

The paper under review studies homoclinic points associated to a hyperbolic fixed point 0 of a planar diffeomorphism \(f\). A special kind of order is introduced to the countable set \(C_ p\) which consists of the transverse homoclinic points that lie on the stable segment from 0 to a transverse homoclinic point \(p\). The authors then derive a numerical conjugacy invariant \(\alpha(f)\) from this order, and prove that \(\alpha(f)\) is a lower bound for the topological entropy of \(f\). They also indicate a method by which good lower bounds on the entropy of \(f\) can be computed numerically.