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Codimension 3 Non-resonant Bifurcations of Rough Heteroclinic Loops with One Orbit Flip*

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Abstract

Heteroclinic bifurcations in four dimensional vector fields are investigated by setting up a local coordinates near a rough heteroclinic loop. This heteroclinic loop has a principal heteroclinic orbit and a non-principal heteroclinic orbit that takes orbit flip. The existence, nonexistence, coexistence and uniqueness of the 1-heteroclinic loop, 1-homoclinic orbit and 1-periodic orbit are studied. The existence of the two-fold or three-fold 1-periodic orbit is also obtained.

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Author information

Correspondence to Shuliang Shui.

Additional information

Project supported by the National Natural Science Foundation of China (No.10471087) and the Zhejiang Provincial Natural Science Foundation of China (No.Y605044).

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Shui, S., Zhu, D. Codimension 3 Non-resonant Bifurcations of Rough Heteroclinic Loops with One Orbit Flip*. Chin. Ann. Math. Ser. B 27, 657–674 (2006). https://doi.org/10.1007/s11401-005-0472-6

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Keywords

  • Bifurcation
  • Heteroclinic loop
  • Non-resonance
  • Orbit flip
  • Periodic orbit

2000 MR Subject Classification

  • 34C37
  • 37C29
  • 34C23