Abstract

By a theorem of P. Hartman (1960), all the smooth contraction diffeomorphisms in finite dimensional spaces can be (locally) linearized in the class $C1$. In this talk we will present a motivation for the extension of this type of result to infinite dimensional Banach spaces. This motivation comes from PDE problems. And we will review the existing results in this direction. A recent example will also be presented that shows that Hartman′s theorem does not extend to infinite dimensions without extra hypotheses.