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Topological entropy of m-fold maps

Published online by Cambridge University Press:  09 February 2005

JOZEF BOBOK  and
ZBIGNIEW NITECKI
JOZEF BOBOK
Affiliation:
KM FSv. ČVUT, Thákurova 7, 166 29 Praha 6, Czech Republic (e-mail: bobok@mat.fsv.cvut.cz)
ZBIGNIEW NITECKI
Affiliation:
Department of Mathematics, Tufts University, Medford, MA 02155, USA (e-mail: zbigniew.nitecki@tufts.edu)
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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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 25 , Issue 2 , April 2005 , pp. 375 - 401
Copyright
2005 Cambridge University Press

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