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Bifurcation of degenerate homoclinic orbits to saddle-center in reversible systems

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Abstract

The authors study the bifurcation of homoclinic orbits from a degenerate homoclinic orbit in reversible system. The unperturbed system is assumed to have saddle-center type equilibrium whose stable and unstable manifolds intersect in two-dimensional manifolds. A perturbation technique for the detection of symmetric and nonsymmetric homoclinic orbits near the primary homoclinic orbits is developed. Some known results are extended.

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Authors and Affiliations

  1. Department of Mathematics, East China Normal University, Shanghai, 200241, China

    Xingbo Liu & Deming Zhu

Authors
  1. Xingbo Liu
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  2. Deming Zhu
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Correspondence to Xingbo Liu.

Additional information

Project supported by the National Natural Science Foundation of China (No. 10671069) and the Shanghai Leading Academic Discipline Project (No. B407).

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Liu, X., Zhu, D. Bifurcation of degenerate homoclinic orbits to saddle-center in reversible systems. Chin. Ann. Math. Ser. B 29, 575–584 (2008). https://doi.org/10.1007/s11401-008-0038-5

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  • DOI: https://doi.org/10.1007/s11401-008-0038-5

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