### Abstract

Original language | English |
---|---|

Pages (from-to) | 463-485 |

Number of pages | 23 |

Journal | Documenta Mathematica |

Volume | 4 |

Publication status | Published - 1999 |

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### Cite this

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

Research output: Contribution to journal › Article

*Documenta Mathematica*, vol. 4, pp. 463-485.

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TY - JOUR

T1 - A Subshift of Finite Type in the Takens-Bogdanov Bifurcation with D 3 Symmetry

AU - Matthies, Karsten

PY - 1999

Y1 - 1999

N2 - 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.

AB - 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.

UR - http://www.mathematik.uni-bielefeld.de/documenta/vol-04/14.html

M3 - Article

VL - 4

SP - 463

EP - 485

JO - Documenta Mathematica

JF - Documenta Mathematica

SN - 1431-0643

ER -