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Topological entropy of m-fold maps

  • JOZEF BOBOK (a1) and ZBIGNIEW NITECKI (a2)

Abstract

We investigate the relation between preimage multiplicity and topological entropy for continuous maps. An argument originated by Misiurewicz and Przytycki shows that if every regular value of a C1 map has at least m preimages then the topological entropy of the map is at least log m. For every integer, there exist continuous maps of the circle with entropy 0 for which every point has at least m preimages. We show that if in addition there is a positive uniform lower bound on the diameter of all pointwise preimage sets, then the entropy is at least log m.

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Topological entropy of m-fold maps

  • JOZEF BOBOK (a1) and ZBIGNIEW NITECKI (a2)

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