Results are presented from a study of manifestations of the activity of the dwarf Gl 414A of spectral class K7 with two planets, one of which (the planet Gl 414A b) with an eccentricity e=0.45 was found to be within the habitable zone over a large part of its orbit. Our analysis showed that the most reliable determination of the rotation period of Gl 414A was obtained from an analysis of photometric observations of the star in the KELT (Kilodegree Extremely Little Telescope) survey which yield a rotation period of P=42 days. However, the existence of this period is not confirmed by periodograms constructed from other observations of Gl 414A. The long-term activity cycle of the star is on the order of 3800 days (10.4 years). The obtained data on the activity of the star were used to estimate the loss of matter from the atmosphere of the planet Gl 414A b using an approximation formula for a model of atmospheric loss with a limit on energy. Based on 486 estimates of the parameter S_HK, the loss of matter by the atmosphere of Gl 414A b over an interval of 5805 days (15.9 years) was calculated. The magnitude of these losses mainly lies within a range of log(M_loss) from 7.15 to 7.50 with a median of 7.30. For an eccentricity of 0.45 the distance from the central star to Gl 414A b ranges from 0.13 to 0.34 a.u., and for these distances the estimated losses of matter by the atmosphere are 16.21·10¹⁷ and 2.37·10¹⁷ g/s, respectively.

结果是对光谱级 K7 的矮星 Gl 414A 与两颗行星的活动表现的研究得出的，其中一颗行星（行星 Gl 414A b）的偏心率 e=0.45，被发现在宜居带内超过了其轨道的很大一部分。我们的分析表明，对 GL 414A 自转周期最可靠的确定是通过对 KELT（千度极小望远镜）巡天中恒星的光度观测进行分析而获得的，得出的自转周期为 P=42 天。然而，根据 GI 414A 的其他观测结果构建的周期图并未证实该周期的存在。恒星的长期活动周期约为3800天（10.4年）。所获得的恒星活动数据用于利用能量限制的大气损失模型的近似公式来估计 Gl 414A b 行星大气中的物质损失。基于参数 S 的 486 次估计_HK，计算了 5805 天（15.9 年）内 GL 414A b 大气层的物质损失。_{这些损失的大小主要集中在从 7.15 到 7.50 的 log(M loss} )范围内，中位数为 7.30。对于 0.45 的偏心率，从中心恒星到 GL 414A b 的距离范围为 0.13 至 0.34 au，对于这些距离，大气造成​​的物质损失估计分别为 16.21·10 17 和 2.37·10 17 ^g / ^s。