**
ACTA MATHEMATICA UNIVERSITATIS COMENIANAE **

Vol. 63, 2 (1994)

pp. 227-239

ON THE STRUCTURE OF MINIMAL ATTRACTION CENTERS OF RECURRENT TRAJECTORIES OF CONTINUOUS MAPS OF THE INTERVAL

A. G. SIVAK

**Abstract**.
We study the structure of minimal attraction centers of recurrent trajectories of continuous maps of the interval, i.e. trajectories of points, which belong to their $\omega$-limit sets. We establish sufficient conditions, under which a pair of closed sets is realizable as the pair of the $\omega$-limit set and the minimal attraction center of a recurrent trajectory of a continuous map. The case when these conditions are necessary and are not sufficient is also discussed and corresponding examples are suggested.

**AMS subject classification**.

**Keywords**.

**Download:** Adobe PDF Compressed Postscript

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 2001, ACTA MATHEMATICA
UNIVERSITATIS COMENIANAE