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Topological entropy of $m$-fold maps on trees

Published online by Cambridge University Press:  17 April 2007

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

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We establish the analogue for maps on trees of the result established by Bobok (Studia Math.152 (2002), 249–261 and Studia Math.166 (2005), 11–27) for interval maps, that a continuous self-map for which all but countably many points have at least $m$ preimages (and none have less than two) has topological entropy bounded below by $\log m$.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 27 , Issue 3 , June 2007 , pp. 671 - 701
Copyright
2007 Cambridge University Press