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Title: On local and global aspects of the 1:4 resonance in the conservative cubic Hénon maps
Author: Gonchenko, Marina
Gonchenko, S. V.
Ovyannnikov, I.
Vieiro Yanes, Arturo
Keywords: Sistemes dinàmics complexos
Complex dynamical systems
Issue Date: 2018
Publisher: American Institute of Physics
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.
Note: Reproducció del document publicat a:
It is part of: Chaos, 2018, vol. 28, num. 4, p. 043123
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ISSN: 1054-1500
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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