Symbolic Extensions and Smooth Dynamical Systems

  title={Symbolic Extensions and Smooth Dynamical Systems},
  author={T. Downarowicz and S. J. Newhouse},
Let f : X → X be a homeomorphism of the compact metric space X. A symbolic extension of (f,X) is a subshift on a finite alphabet (g, Y ) which has f as a topological factor. We show that a generic C1 non-hyperbolic (i.e.,non-Anosov) area preserving diffeomorphism of a compact surface has no symbolic extensions. For r > 1, we exhibit a residual subset R of an open set U of Cr diffeomorphisms of a compact surface such that if f ∈ R, then any possible symbolic extension has topological entropy… CONTINUE READING
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