A Subshift of Finite Type in the Takens-Bogdanov Bifurcation with D 3 Symmetry

Research output: Contribution to journalArticle

Abstract

We study the versal unfolding of a vector field of codimension two, that has an algebraically double eigenvalue 0 in the linearisation of the origin and is equivariant under a representation of the symmetry group D 3. A subshift of finite type is encountered near a clover of homoclinic orbits. The subshift encodes the itinerary along the three different homoclinic orbits. In this subshift all those symbol sequences are realized for which consecutive symbols are different. In the parameter space we also locate a transcritical, three different Hopf and two global (homoclinic) bifurcations.
Original languageEnglish
Pages (from-to)463-485
Number of pages23
JournalDocumenta Mathematica
Volume4
Publication statusPublished - 1999

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Bogdanov-Takens Bifurcation
Subshift
Finite Type
Homoclinic Orbit
Symmetry
Homoclinic Bifurcation
Global Bifurcation
Unfolding
Symmetry Group
Equivariant
Codimension
Linearization
Parameter Space
Consecutive
Vector Field
Eigenvalue

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A Subshift of Finite Type in the Takens-Bogdanov Bifurcation with D 3 Symmetry. / Matthies, Karsten.

In: Documenta Mathematica, Vol. 4, 1999, p. 463-485.

Research output: Contribution to journalArticle

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