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Mixed dynamics of two-dimensional reversible maps with a symmetric couple of quadratic homoclinic tangencies

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We study dynamics and bifurcations of 2-dimensional reversible maps having a symmetric saddle fixed point with an asymmetric pair of nontransversal homoclinic orbits (a symmetric nontransversal homoclinic figure-8). We consider one-parameter families of reversible maps unfolding the initial homoclinic tangency and prove the existence of infinitely many sequences (cascades) of bifurcations related to the birth of asymptotically stable, unstable and elliptic periodic orbits.

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American Institute of Mathematical Sciences (AIMS)

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Discrete and Continuous Dynamical Systems-Series A, 2018, vol. 38, num. 9, p. 4483-4507

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(c) American Institute of Mathematical Sciences (AIMS), 2018

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Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
Mixed dynamics of two-dimensional reversible maps with a symmetric couple of quadratic homoclinic tangencies