Homoclinic Tangencies To Resonant Saddles And Discrete Lorenzat Tractors

We study bifurcations of periodic orbits in three parameter general unfoldings of certain types quadratic homoclinic tangencies to saddle fi xed points. We apply the rescaling technique to fi rst return ( Poincare) maps and show that the rescaled maps can be brought to a map asymptotically close to the 3D Henon map (x) over bar = y; (y) over bar = z; (x) over bar = M-1 + M-2y + Bx - z(2) which, as known [14], exhibits discrete Lorenz attractors in some open domains of the parameters. Based on this, we prove the existence of in finite cascades of systems possessing discrete Lorenz attractors near the original diffeomorphism.