ZHANG Tian-si, ZHU De-ming. Bifurcations of Double Homoclinic Flip Orbits With Resonant Eigenvalues[J]. Applied Mathematics and Mechanics, 2007, 28(11): 1353-1362.
Citation: ZHANG Tian-si, ZHU De-ming. Bifurcations of Double Homoclinic Flip Orbits With Resonant Eigenvalues[J]. Applied Mathematics and Mechanics, 2007, 28(11): 1353-1362.

Bifurcations of Double Homoclinic Flip Orbits With Resonant Eigenvalues

  • Received Date: 2006-08-29
  • Rev Recd Date: 2007-08-06
  • Publish Date: 2007-11-15
  • Concerns double homoclinic loops with or bitflips and two resonant eigenvalues in a fourdimensional system. We use the solution of a normal form system to construct a singular map in some neighborhood of the equilibrium, and the solution of a linear variational system to construct a regular map in some neighborhood of the double homoclinic loops, then compose them to get the important Poincar map. A simple calculation gives explicitly an expression of the associated successor function. By a delicate analysis of the bifurcation equation, we obtain the condition that the original double homoclinic loops are kept, and prove the existence and the existence regions of the large 1-homo clinic orbit bifurcation surface, 2-fold large 1-periodic or bit bifurcation surface, large 2-homoclinic or bit bifur cation surface and their appro ximate expressions. We also locate the large periodic orbits and large homoclinic orbits and their number.
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