PROBABILISTIC APPROACH TO HOMOCLINIC CHAOS

Three-dimensional systems posessing a homoclinic orbit associated to a saddle focus with eigenvalues rho +/- iomega, -lambda and giving rise to homoclinic chaos when the Shil'nikov condition rho < lambda is sat isfied are studied. The 2D Poincare map and its 1D contractions captur ing the essential features of the flow are given. At homoclinicity, th ese 1D maps are found to be piecewise linear. This property allows one to reduce the Frobenius-Perron equation to a master equation whose so lution is analytically known. The probabilistic properties such as the time autocorrelation function of the state variable x are explicitly derived.