Geodesic
Rigorous numerics for symmetric homoclinic orbits in reversible dynamical systems
Kybernetika, Tome 43 (2007) no. 6, pp. 797-806.

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We propose a new rigorous numerical technique to prove the existence of symmetric homoclinic orbits in reversible dynamical systems. The essential idea is to calculate Melnikov functions by the exponential dichotomy and the rigorous numerics. The algorithm of our method is explained in detail by dividing into four steps. An application to a two dimensional reversible system is also treated and the existence of a symmetric homoclinic orbit is rigorously verified as an example.
Classification : 34C37, 34D09, 37C29, 37M20, 65G20, 65P30
Keywords: rigorous numerics; exponential dichotomy; homoclinic orbits 
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     author = {Hiraoka, Yasuaki},
     title = {Rigorous numerics for symmetric homoclinic orbits in reversible dynamical systems},
     journal = {Kybernetika},
     pages = {797--806},
     publisher = {mathdoc},
     volume = {43},
     number = {6},
     year = {2007},
     mrnumber = {2388394},
     zbl = {1138.65107},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2007__43_6_a4/}
}
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Hiraoka, Yasuaki. Rigorous numerics for symmetric homoclinic orbits in reversible dynamical systems. Kybernetika, Tome 43 (2007) no. 6, pp. 797-806. http://geodesic.mathdoc.fr/item/KYB_2007__43_6_a4/