Chaos around Hyperbolic Fixed Points

Abstract

Using a simple billiard system we first give a brief review of fundamental properties in an area-preserving mapping and then show, by revealing a mixing mechanism hidden around a hyperbolic fixed point in spite of the integrability theorem proven by Moser (Commun. Pure & Appl. Math. 9 (1956) 673), that chaos originates from homoclinic structures.