A note on the shadowing lemma and symmetric periodic points

Nonlinearity 8 (1995) 1067-1075

Michael Dellnitz and Ian Melbourne


A standard use of shadowing lemmas in dynamical systems theory is to prove density of periodic points. When there is symmetry present it is natural to investigate the density of periodic points of a given symmetry. We obtain several results in this direction. As an application, we prove a result about compact group extensions of hyperbolic and nonuniformly hyperbolic dynamical systems.

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