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On dynamics of triangular maps of the square

Published online by Cambridge University Press:  19 September 2008

S. F. Kolyada
S. F. Kolyada
Affiliation:
Institute of Mathematics, Ukrainian Academy of Sciences, Repin str. 3, 252601 Kiev-4, Ukraine
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Abstract

The paper is devoted to the triangular maps of the square into itself. The results presented were recently obtained by the author and are briefly stated (in Russian) in a difficult paper as well as those (jointly published with A. N. Sharkovsky) published in ECIT-89 (abstract). All these results are systematized and extended by the new ones. The more detailed proofs of all statements are given. It is shown, for example, that triangular maps exist such that their minimal attraction centres do not coincide with the centres, as well as such ones exist that the Milnor attractor is not contained in the closure of the set of periodic points.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 12 , Issue 4 , December 1992 , pp. 749 - 768
Copyright
Copyright © Cambridge University Press 1992

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