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Heterodimensional tangencies on cycles leading to strange attractors

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  • In this paper, we study a two-parameter family $\{\varphi_{\mu,\nu}\}$ 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 subfamily of $\{\varphi_{\mu,\nu}\}$. 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.
    Mathematics Subject Classification: 37D30, 37D45, 37G25.


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