Periodic points of equivariant maps

• Autores: Jerzy Jezierski, Waclaw Marzantowicz
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 107, Nº 2, 2010, págs. 224-248
• Idioma: inglés
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• Resumen

  • We assume that X is a compact connected polyhedron, G is a finite group acting freely on X, and f:X→X a G-equivariant map. We find formulae for the least number of n-periodic points in the equivariant homotopy class of f, i.e., infh|(Fix(hn)| (where h is G-homotopic to f). As an application we prove that the set of periodic points of an equivariant map is infinite provided the action on the rational homology of X is trivial and the Lefschetz number L(fn) does not vanish for infinitely many indices n commeasurable with the order of G. Moreover, at least linear growth, in n, of the number of points of period n is shown.