Chaotic dynamics of three-dimensional Henon maps that originate from a homoclinic bifurcation

We study bifurcations of a three-dimensional diffeomorphism; go, that has a quadratic homoclinic tangency to a saddle-focus fixed point with multipliers (lambda e(i phi), lambda e(-i phi), gamma), where 0 < lambda < 1 < vertical bar gamma vertical bar and vertical bar lambda(2)gamma vertical bar = 1. We show that in a three-parameter family, g(epsilon), of diffeomorphisms close to go, there exist infinitely many open regions near 6 = 0 where the corresponding normal form of the first return map to a neighborhood of a homoclinic point is a three-dimensional Henon-like map. This map possesses, in some parameter regions, a "wild- hyperbolic" Lorenz-type strange attractor. Thus, we show that this homoclinic bifurcation leads to a strange attractor. We also discuss the place that these three-dimensional Henon maps occupy in the class of three-dimensional quadratic maps with constant Jacobian.