Geodesic
A subshift of finite type in the Takens-Bogdanov bifurcation with $D_3$ symmetry
Documenta mathematica, Tome 4 (1999), pp. 463-485
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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 D3​. 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.
DOI : 10.4171/dm/65
Classification : 34C28
Mots-clés : symmetry, Takens-bogdanov, subshift of finite type, homoclinic orbit 
@article{10_4171_dm_65,
     author = {Karsten Matthies},
     title = {A subshift of finite type in the {Takens-Bogdanov} bifurcation with $D_3$ symmetry},
     journal = {Documenta mathematica},
     pages = {463--485},
     year = {1999},
     volume = {4},
     doi = {10.4171/dm/65},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/65/}
}
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Karsten Matthies. A subshift of finite type in the Takens-Bogdanov bifurcation with $D_3$ symmetry. Documenta mathematica, Tome 4 (1999), pp. 463-485. doi: 10.4171/dm/65

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