Exponentially small splitting of homoclinic orbits of parabolic differential equations under periodic forcing
Freie Universität Berlin, Institut für Mathematik I, Arnimallee 2-6, 14195 Berlin, Germany
Homoclinic orbits of semilinear parabolic partial differential equations can split under time-periodic forcing as for ordinary differential equations. The stable and unstable manifold may intersect transverse at persisting homoclinic points. The size of the splitting is estimated to be exponentially small of order exp$(-c/\epsilon)$ in the period $\epsilon$ of the forcing with $\epsilon \rightarrow 0$.
Mathematics Subject Classification: 37L99, 37C29, 37G2.
Citation: Karsten Matthies. Exponentially small splitting of homoclinic orbits of parabolic differential equations under periodic forcing. Discrete & Continuous Dynamical Systems - A, 2003, 9 (3) : 585-602. doi: 10.3934/dcds.2003.9.585
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