Summary
For a transverse homoclinic orbit γ of a mapping (not necessarily invertible) on a Banach space, it is shown that the mapping restricted to orbits near γ is equivalent to the shift automorphism on doubly infinite sequences on finitely many symbols. Implications of this result for the Poincaré map of semiflows are given.
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This work was supported by the Air Force Office of Scientific Research under Grant #81-0198, by the National Science Foundation under Grant #MCS-8205355 and by the Army Research Office under Grant ù DAAG-29-83-K-0029.
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Hale, J.K., Lin, XB. Symbolic dynamics and nonlinear semiflows. Annali di Matematica pura ed applicata 144, 229–259 (1986). https://doi.org/10.1007/BF01760821
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DOI: https://doi.org/10.1007/BF01760821