Ale Jan Homburg and Howard Weiss
A Geometric Criterion for Positive Topological Entropy 
II: Homoclinic Tangencies 
(449K, Postscript)

ABSTRACT.  In a series of important papers \cite{GS1, GS2} Gavrilov 
and Shilnikov established a topological conjugacy between a 
surface diffeomorphism having a dissipative hyperbolic 
periodic point with certain types of {\it quadratic} 
homoclinic tangencies and the full shift on two symbols, 
thus exhibiting horseshoes near a tangential homoclinic 
point. In this note, which should be viewed of as an addendum 
to \cite{BW}, we extend this result by showing that such a 
diffeomorphism with a homoclinic tangency having {\it any} 
order contact, possible with {\it infinite} order contact, 
possesses a horseshoe near the homoclinic point.