**
ACTA MATHEMATICA UNIVERSITATIS COMENIANAE **

Vol. LXXII, 2 (2003)

p. 245 – 251

Triangular Maps with the Chain Recurent Points Periodic

J. Kupka

**Abstract**.
Forti and Paganoni [Grazer Math. Ber. {\bf 339} (1999), 125--140]
found a triangular map $F(x,y)=(f(x),g_x (y))$ from $I\times I$
into itself for which closed set of~periodic points is a proper
subset of the set of chain recurrent points. We asked whether
there is a characterization of triangular maps for which every
chain recurrent point is periodic. We answer this question in
positive by showing that, for a triangular map with closed set of
periodic points and any posi\-tive real~$\varepsilon$, every
$\varepsilon$-chain from a chain recurrent point to itself may be
represented as a finite union of $\varepsilon$-chains whose all
points either are periodic or form a nontrivial
$\varepsilon$-chain of some one-dimensional map~$g_x$.

**AMS subject classification**:
37E99, 37B20, 26A18, 54H20;

**Keywords**:
Triangular maps, periodic points, chain recurrent
points

**Download:** Adobe PDF Compressed Postscript

**Version to read:** Adobe PDF

Acta Mathematica Universitatis Comenianae

Institute of Applied Mathematics

Faculty of Mathematics, Physics and Informatics

Comenius University

842 48 Bratislava, Slovak Republic

Telephone: + 421-2-60295111 Fax: + 421-2-65425882

e-Mail: amuc@fmph.uniba.sk
Internet: www.iam.fmph.uniba.sk/amuc
©
Copyright 2003, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE