<p>This manuscript defines a notion of Lyapunov stability for semigroup actions on Hausdorff spaces not requiring any metric or uniformity. It introduces a local version of stable set and shows how Lyapunov’s ideas can be generally applicable to simpler topologies. Various aspects of stability and attraction are related.</p>

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Lyapunov stability of transformation semigroups on Hausdorff spaces

  • Victor H. L. Rocha,
  • Josiney A. Souza,
  • Ronan A. Reis

摘要

This manuscript defines a notion of Lyapunov stability for semigroup actions on Hausdorff spaces not requiring any metric or uniformity. It introduces a local version of stable set and shows how Lyapunov’s ideas can be generally applicable to simpler topologies. Various aspects of stability and attraction are related.