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Dynamics of homeomorphisms on minimal sets generated by triangular mappings

Published online by Cambridge University Press:  17 April 2009

Gian Luigi Forti ,
Luigi Paganoni  and
Jaroslav Smítal
Gian Luigi Forti
Affiliation:
Dipartimento di Matematica, Università degli Studi di Milano, via C. Saldini 50, 20133 Milano, Italy
Luigi Paganoni
Affiliation:
Dipartimento di Matematica, Università degli Studi di Milano, via C. Saldini 50, 20133 Milano, Italy
Jaroslav Smítal
Affiliation:
Institute of Mathematics, Silesian University, 74601 Opava, Czech Republuc
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Abstract

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The main goal of the paper is the construction of a triangular mapping F of the square with zero topological entropy, possessing a minimal set M such that F|M is a strongly chaotic homeomorphism, as well as other properties that are impossible for continuous maps on an interval.

To do this we define a parametric class of triangular maps on Q × I, where Q is an infinite minimal set on the interval, which are extendable to continuous triangular maps F: I2 → I2. This class can be used to create other examples.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 59 , Issue 1 , February 1999 , pp. 1 - 20
Copyright
Copyright © Australian Mathematical Society 1999

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