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A remark about Sil'nikov saddle-focus homoclinic orbits

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  • In this note we study Sil'nikov saddle-focus homoclinic orbits paying particular attention to four and higher dimensions where two additional conditions are needed. We give equivalent conditions in terms of subspaces associated with the variational equation along the orbit. Then we review Rodriguez's construction of a three-dimensional system with Sil'nikov saddle-focus homoclinic orbits and finally show how to construct higher-dimensional systems with such orbits.
    Mathematics Subject Classification: Primary: 34C27; 37G20; Secondary: 34C28.


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