Exponential dichotomies, the shadowing lemma and homo clinic orbits in Banach spaces (Resenhas do Instituto de Matemática e Estatística da Universidade de São Paulo, 2014)
We prove infinite-dimensional versions of theshadowing lenuna and Smale's theorem ( for a transverse homoclinic orbit) of a C1 map, not a diffeomorphism, using thenotion of an exponential dichotomy.