Topological entropy of shift function on the sequences space induced by expanding piecewise linear transformations

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January 2002, 8(1): 191-208. doi: 10.3934/dcds.2002.8.191

Topological entropy of shift function on the sequences space induced by expanding piecewise linear transformations

1.	Department of Mathematics, Faculty of Mathematics and Natural Sciences, Gadjah Mada University, Sekip Utara, Yogyakarta, Indonesia

Received October 2000 Revised September 2001 Published October 2001

Abstract
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Let $I = [0, 1]$. The topological entropy of shift function on the sequences space induced by a piecewise linear transformation from $I$ into itself is studied. The main goal of the paper is to investigate the relation between the topological entropy of piecewise linear transformations which in general are not continuous, and the topological entropy of shift function which the transformation induces on a space of symbol sequences. The main result is that for a class of piecewise linear (possibly discontinuous) self-maps of $I$, the topological entropy coincides with the topological entropy of shift function which the map induces on a space of symbol sequences.

Keywords: topological entropy, Piecewise linear transformation, sequences space., shift function.

Mathematics Subject Classification: 58F0.

Citation: Prof. Dr.rer.nat Widodo. Topological entropy of shift function on the sequences space induced by expanding piecewise linear transformations. Discrete & Continuous Dynamical Systems - A, 2002, 8 (1) : 191-208. doi: 10.3934/dcds.2002.8.191

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