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

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

1999-01-06

arxiv.org/abs/chao-dyn/9901004v1

Nonlinear Sciences

Chaotic Dynamics

6 pages, LaTeX

Scientific paper

10.1143/PTP.101.1181

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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