Symbolic dynamics and nonlinear semiflows (Q1095473)

The authors generalize results of Smale and of Shil'nikov about diffeomorphisms of manifolds to results about semiflows in Banach spaces. Smale showed that if q is a transverse homoclinic point then for some power of the map there is a ``horseshoe'' near the homoclinic point. This means that on this set the map is equivalent to a full 2 sided shift on two symbols. The authors generalize the necessary definitions and prove analogous results for semiflows on Banach spaces. They then discuss some of the consequences.