Abundance of attracting, repelling and elliptic periodic orbits in two-dimensional reversible maps
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We study dynamics and bifurcations of two-dimensional reversible maps having non-transversal heteroclinic cycles containing symmetric saddle fixed points. We consider one-parameter families of reversible maps unfolding the initial heteroclinic tangency and prove the existence of infinitely many sequences (cascades) of bifurcations and birth of asymptotically stable, unstable and elliptic periodic orbits
CitationDelshams, A. [et al.]. Abundance of attracting, repelling and elliptic periodic orbits in two-dimensional reversible maps. "Nonlinearity", 01 Gener 2013, vol. 26, p. 1-33.