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2018

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/145025

On local and global aspects of the 1:4 resonance in the conservative cubic Hénon maps

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https://doi.org/10.1063/1.5022764

Abstract

We study the 1:4 resonance for the conservative cubic Henon maps C6 with positive and negative cubic terms. These maps show up different bifurcation structures both for fixed points with eigenvalues 6i and for 4-periodic orbits. While for C-, the 1:4 resonance unfolding has the so-called Arnold degeneracy [the first Birkhoff twist coefficient equals (in absolute value) to the first resonant term coefficient], the map Cþ has a different type of degeneracy because the resonant term can vanish. In the last case, non-symmetric points are created and destroyed at pitchfork bifurcations and, as a result of global bifurcations, the 1:4 resonant chain of islands rotates by p/4. For both maps, several bifurcations are detected and illustrated.

Subject

Sistemes dinàmics complexos, Ressonància

Subject (English)

Complex dynamical systems, Resonance

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Articles publicats en revistes (Matemàtiques i Informàtica)

Citation

GONCHENKO, Marina, et al. On local and global aspects of the 1:4 resonance in the conservative cubic Hénon maps. Chaos. 2018. Vol. 28, num. 4, pags. 043123. ISSN 1054-1500. [consulted: 10 of June of 2026]. Available at: https://hdl.handle.net/2445/145025

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