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

# metadata.dc.description.abstract[].value
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.

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(c) American Institute of Physics , 2018

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Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
On local and global aspects of the 1:4 resonance in the conservative cubic Hénon maps