The aim of this work is the study of the asymptotic dynamical behaviour, of solutions that approach parabolic fixed points in difference equations. In one dimensional difference equations, we present the asymptotic development for positive solutions tending to the fixed point. For higher dimensions, through the study of two families of difference equations in the two and three dimensional case, we take a look at the asymptotic dynamic behaviour. To show the existence of solutions we rely on the parametrization method.

中文翻译：

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具有抛物线平衡的差分方程的渐近动力学

这项工作的目的是研究渐近动力学行为，研究在差分方程中接近抛物线不动点的解。在一维差分方程中，我们给出了趋于固定点的正解的渐近发展。对于更高的维度，通过研究二维和三维情况下的两个差分方程族，我们来研究渐近动力学行为。为了显示解决方案的存在，我们依赖于参数化方法。