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MATHEMATICA BOHEMICA, Vol. 125, No. 3, pp. 275-306 (2000)
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# On condensing discrete dynamical systems

## Valter Seda

* Valter Seda*, Faculty of Mathematics and Physics, Comenius University, Mlynska dolina, 842 15 Bratislava, Slovak Republic, e-mail: ` seda@fmph.uniba.sk`

**Abstract:**
In the paper the fundamental properties of discrete dynamical systems generated by an $\alpha $-condensing mapping ($\alpha $ is the Kuratowski measure of noncompactness) are studied. The results extend and deepen those obtained by M. A. Krasnosel'skij and A. V. Lusnikov in \cite {21}. They are also applied to study a mathematical model for spreading of an infectious disease investigated by P. Takac in \cite {35}, \cite {36}. \endabstract

**Keywords:** condensing discrete dynamical system, stability, singular interval, continuous branch connecting two points, continuous curve

**Classification (MSC2000):** 58F08, 47H07, 47H10, 34C25, 58F22

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