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May  2003, 9(3): 585-602. doi: 10.3934/dcds.2003.9.585

Exponentially small splitting of homoclinic orbits of parabolic differential equations under periodic forcing

Karsten Matthies 1,

1. 

Freie Universität Berlin, Institut für Mathematik I, Arnimallee 2-6, 14195 Berlin, Germany

Received  November 2001 Revised  December 2002 Published  February 2003

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 $\epsilon \rightarrow 0$.
Keywords: exponential smallness., semilinear parabolic equations, splitting, Homoclinic orbit.
Mathematics Subject Classification: 37L99, 37C29, 37G2.
Citation: Karsten Matthies. Exponentially small splitting of homoclinic orbits of parabolic differential equations under periodic forcing. Discrete and Continuous Dynamical Systems, 2003, 9 (3) : 585-602. doi: 10.3934/dcds.2003.9.585
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