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.

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