Transversal homoclinic orbits for higher dimensional difference equations |
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| Authors: | Weiyao Zeng Michal Fečkan |
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| Institution: | Department of Mathematics , Changsha Railway University , Changsha, Hunan, 410007, People's Republic of China |
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| Abstract: | In this paper, we use the functional analytic method (theory of exponential dichotomies and Liapunov-Schmidt method) to study the homoclinic bifurcations of higher dimensional difference equations in a degenerate case. We obtain a Melnikov vector mapping for difference equations with the help of which the existence of transversal homoclinic orbits can be detected. |
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| Keywords: | Exponential dichotomies Transversal homoclinic orbits Difference equations Melnikov vector mapping Degenerate case |
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