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On topological entropy of triangular maps of the square

Published online by Cambridge University Press:  17 April 2009

Lluís Alsedà ,
Sergiĭ F. Kolyada  and
Ľubomír Snoha
Lluís Alsedà
Affiliation:
Departament de Matemàtiques, Universitat Autònoma, de Barcelona 08193 – Bellaterra Barcelona, Spain
Sergiĭ F. Kolyada
Affiliation:
Department of Mathematics Faculty of Education Tajovského 40 975 49 Banská Bystrica, Czechoslovakia
Ľubomír Snoha
Affiliation:
Institute of Mathematics, Ukrainian Academy of Sciences Repin str.3 252601 Kiev - 4, Ukraine
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We study the topological entropy of triangular maps of the square. We show that such maps differ from the continuous maps of the interval because there exist triangular maps of the square of “type 2∞” with infinite topological entropy. The set of such maps is dense in the space of triangular maps of “type at most 2∞” and the topological entropy as a function of the triangular maps of the square is not lower semicontinuous. However, we show that for these maps the characterisation of the lower bounds of the topological entropy depending on the set of periods is the same as for the continuous maps of the interval.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 48 , Issue 1 , August 1993 , pp. 55 - 67
Copyright
Copyright © Australian Mathematical Society 1993

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