Codimension 2 Symmetric Homoclinic Bifurcations and Application to 1:2 Resonance
1990 ◽
Vol 42
(2)
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pp. 191-212
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Keyword(s):
In this paper we study a codimension 3 form of the 1:2 resonance. It was first noted by Arnold [3] that the study of bifurcations of symmetric vector fields under a rotation of order q yields information about Hopf bifurcation for a fixed point of a planar diffeomorphism F with eigenvalues . The map Fq can be identified to arbitrarily high order with the flow map of a symmetric vector field having a double-zero eigenvalue ([3], [4], [10], [23]). The resonance of order 2 (also called 1:2 resonance) considered here is the case of a pair of eigenvalues —1 with a Jordan block of order 2. The diffeomorphism then has normal form around the origin given by [4]:
2010 ◽
Vol 20
(04)
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pp. 995-1005
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Keyword(s):
1996 ◽
Vol 16
(6)
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pp. 1147-1172
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Keyword(s):
2009 ◽
Vol 19
(06)
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pp. 2115-2121
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Keyword(s):
2012 ◽
Vol 23
(5)
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pp. 555-562
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2018 ◽
Keyword(s):
1999 ◽
Vol 121
(1)
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pp. 101-104
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Keyword(s):
2019 ◽
Vol 16
(11)
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pp. 1950180
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1991 ◽
Vol 11
(3)
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pp. 443-454
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1999 ◽
Vol 121
(1)
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pp. 105-109
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