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2018-08

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/194449

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

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https://doi.org/10.3934/dcds.2018196

Abstract

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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Teoria de la bifurcació, Sistemes dinàmics diferenciables, Equacions diferencials ordinàries

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Bifurcation theory, Differentiable dynamical systems, Ordinary differential equations

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DELSHAMS VALDÉS, Amadeu, et al. Mixed dynamics of two-dimensional reversible maps with a symmetric couple of quadratic homoclinic tangencies. Discrete and Continuous Dynamical Systems-Series A. 2018. Vol. 38, num. 9, pags. 4483-4507. ISSN 1078-0947. [consulted: 9 of June of 2026]. Available at: https://hdl.handle.net/2445/194449

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