HETERODIMENSIONAL TANGENCIES ON CYCLES LEADING TO STRANGE ATTRACTORS

In this paper, we study a two-parameter family {phi(mu,nu)} of three dimensional diffeomorphisms which have a bifurcation induced by simultaneous generation of a heterodimensional cycle and a heterodimensional tangency associated to two saddle points. We show that such a codimension-2 bifurcation generates a quadratic homoclinic tangency associated to one of the saddle continuations which unfolds generically with respect to some one-parameter sub-family of{phi(mu,nu)}. Moreover, from this result together with some well-known facts, we detect some nonhyperbolic phenomena (i.e., the existence of nonhyperbolic strange attractors and the C-2 robust tangencies) arbitrarily close to the codimension-2 bifurcation.