Exponentially small oscillation of 2-dimensional stable and unstable manifolds in 4-dimensional symplectic mappings
Yoshihiro Hirata, Kazuhiro Nozaki, Tetsuro Konishi
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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