Symbolic dynamics and nonlinear semiflows

Abstract

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. © 1986 Fondazione Annali di Matematica Pura ed Applicata.