The SYM-H and AE geomagnetic indices can be considered as proxies of the response of the Earth’s magnetosphere and ionosphere to solar magnetic activity. They indirectly monitor some electric current systems which flow in the ionosphere and magnetosphere whose dynamics are directly or indirectly related to the Sun–Earth interaction. Consequently, their temporal changes reflect processes occurring in the near-Earth space, which contribute differently to the overall magnetosphere–ionosphere dynamics. The aim of this work is to characterize the nature of these two geomagnetic indices by following a complex system approach and applying a novel formalism, e.g., the EMD-based dominant amplitude multifractal formalism (EMD-DAMF). A set of complexity measures, i.e., the Hurst exponent ($\mathcal{H}$), the singularity width ($\Delta \alpha$) and the spectrum width ($\Delta f$), is evaluated for both geomagnetic indices analyzing data recorded during the last two solar cycles. One of the most significant findings of this study is the absence of relevant differences between the two solar cycles in terms of complexity measures for both geomagnetic indices, suggesting that only the occurrence and the frequency of geomagnetic storms and substorms affect the Hurst exponent and the singularity widths of SYM-H and AE indices. Moreover, while the AE index complexity measures do not show a significant dependence on geomagnetic activity, the SYM-H index shows a reduction in its complexity features during the geomagnetic storms, manifesting a more persistent behavior and moving from a (mono)fractal-like to a multifractal-like behavior when passing from quiet to disturbed periods. Finally, our findings are consistent with previous works on the forecast horizon of the geomagnetic activity as well as on the relation between the high-latitude ionosphere and the low-latitude magnetosphere, thus confirming the importance of providing higher resolution measures for correctly dealing with several Space Weather phenomena.

SYM-H和AE地磁指数可以看作是地球磁层和电离层对太阳磁活动的响应的代理。他们间接地监测在电离层和磁层中流动的某些电流系统，它们的动力学直接或间接地与日地相互作用有关。因此，它们的时间变化反映了近地空间中发生的过程，这些过程对整个磁层-电离层动力学的贡献不同。这项工作的目的是通过遵循复杂的系统方法并应用一种新颖的形式主义（例如，基于EMD的主导振幅多重分形形式主义（EMD-DAMF））来表征这两个地磁指数的性质。一组复杂性度量，即Hurst指数（$\mathcal{H}$），奇异宽度（$\Delta \alpha$）和频谱宽度（$\Delta F$），以评估在过去两个太阳周期内记录的两个地磁指数分析数据。这项研究最重要的发现之一是，就两个地磁指数的复杂性衡量而言，两个太阳周期之间都没有相关的差异，这表明只有地磁暴和亚暴的发生和频率会影响赫斯特指数和奇异性。 SYM-H和AE索引的宽度。此外，虽然AE指数的复杂性指标并未显示出对地磁活动的显着依赖性，但SYM-H指数显示出在地磁风暴期间其复杂性特征有所降低，表现出更持久的行为并摆脱了类似（单）分形的现象。从安静期到扰动期时会呈现类似多重分形的行为。最后，