Symbolic dynamics and nonlinear semiflows. (English) Zbl 0632.58027

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.
Reviewer: B.Kitchens


37D99 Dynamical systems with hyperbolic behavior
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