Homoclinic bifurcations in the unfolding of the nilpotent singularity of codimension 4 in R4
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Servicio de Publicaciones de la Universidad de Oviedo
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The rich variety of homoclinic phenomena exhibited by the limit family of any generic unfolding of a fourdimensional nilpotent singularity of codimension-four is discussed. Specifically, numerical techniques based on the Taylor integrator and the expansion of the invariant manifolds were designed for this family. A partial bifurcation diagram which includes, besides a suggestive catalogue of local bifurcations of equilibria, folds and period doublings of periodic orbits is also given. These results are certainly the first steps towards a much more ambitious goal: to achieve a general understanding of these codimension-four unfoldings.
The rich variety of homoclinic phenomena exhibited by the limit family of any generic unfolding of a fourdimensional nilpotent singularity of codimension-four is discussed. Specifically, numerical techniques based on the Taylor integrator and the expansion of the invariant manifolds were designed for this family. A partial bifurcation diagram which includes, besides a suggestive catalogue of local bifurcations of equilibria, folds and period doublings of periodic orbits is also given. These results are certainly the first steps towards a much more ambitious goal: to achieve a general understanding of these codimension-four unfoldings.
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The authors has been partially supported by the project MINECO-18-MTM2017-87697-P.
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