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Exponentially small oscillation of 2-dimensional stable and unstable manifolds in 4-dimensional symplectic mappings

Yoshihiro Hirata·Kazuhiro Nozaki·Tetsuro Konishi
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Abstract

Homoclinic bifurcation of 4-dimensional symplectic mappings is asymptotically studied. We construct the 2-dimensional stable and unstable manifolds near the sub-manifolds which experience exponentially small splitting, and successfully obtain exponentially small oscillating terms in the 2-dimensional manifolds.

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Yoshihiro Hirata, Kazuhiro Nozaki, Tetsuro Konishi. 1999-01-06. Exponentially small oscillation of 2-dimensional stable and unstable manifolds in 4-dimensional symplectic mappings. https://doi.org/10.1143/ptp.101.1181

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