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### Published volumes

##### 1936-1944
Families of transitive maps on $\mathbb{R}$ with horizontal asymptotes
Volume 59, no. 2 (2018), pp. 375–387

DOI: https://doi.org/10.33044/revuma.v59n2a08

### Abstract

We will prove the existence of a class of transitive maps on the real line $\mathbb{R}$, with a discontinuity and horizontal asymptotes, whose set of periodic orbits is dense in $\mathbb{R}$; that is, a class of chaotic families. In addition, we will show a rare phenomenon: the existence of periodic orbits of period three prevents the existence of transitivity.