Purpose:

To build one-dimensional chaotic dynamical systems through the study of functions with domain and codomain in the interval [0, 1] which is defined in terms of four parameters.

Methodology:

Based on the parameters that define each function that is proposed, those which have period three were identified and which induce a chaotic system in the context of Li-Yorke. The fixed point and Sharkovskii theorems were the fundamental tools in this work.

Results:

We obtained a set of chaotic dynamic systems. In turn, we described a simple process in order to obtain chaotic dynamic systems (additional to those obtained) and we suggest, as a first application, the obtainment of pseudo-random numbers.

Limitations:

The dynamic systems that were built are chaotic in the Li-Yorke sense -not necessarily in the Devaney sense-.

Findings:

The functions that were studied have a Zeta form graphic, and for each of those we identified its respective dual (the obtained graphics present a symmetric relation) and that is how we show the conditions that must verify the parameters -primal and dual- in order to obtain (or not) period three.

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