Liapunov stability and adding machines

  title={Liapunov stability and adding machines},
  author={J. Buescu and I. Stewart},
  journal={Ergodic Theory and Dynamical Systems},
  • J. Buescu, I. Stewart
  • Published 1995
  • Mathematics
  • Ergodic Theory and Dynamical Systems
  • In Chapter 1 we discussed several notions of stability for compact invariant sets of dynamical systems. Here we shall prove that, under very general hypotheses, the set of connected components of a stable set of a discrete dynamical system possesses a tightly constrained structure. More precisely, suppose that X is a locally compact, locally connected metric space, f: X → X is a continuous mapping (not necessarily invertible) and A is a compact transitive set. Let $\overset{\lower0.5em\hbox… CONTINUE READING
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