Ibañez Bustos, R. V.R. V.Ibañez BustosBuccino, A. P.A. P.BuccinoMessina, S.S.MessinaLANZA, Antonino FrancescoAntonino FrancescoLANZAMauas, P. J. D.P. J. D.Mauas2021-01-122021-01-1220200004-6361http://hdl.handle.net/20.500.12386/29680Recently, new debates about the role of layers of strong shear have emerged in stellar dynamo theory. Further information on the long-term magnetic activity of fully convective stars could help determine whether their underlying dynamo could sustain activity cycles similar to the solar one. We performed a thorough study of the short- and long-term magnetic activity of the young active dM4 star Gl 729. First, we analyzed long-cadence $K2$ photometry to characterize its transient events (e.g., flares) and global and surface differential rotation. Then, from the Mount Wilson $S$-indexes derived from CASLEO spectra and other public observations, we analyzed its long-term activity between 1998 and 2020 with four different time-domain techniques to detect cyclic patterns. Finally, we explored the chromospheric activity at different heights with simultaneous measurements of the H$\alpha$ and the Na I D indexes, and we analyzed their relations with the $S$-Index. We found that the cumulative flare frequency follows a power-law distribution with slope $\sim- 0.73$ for the range $10^{32}$ to $10^{34}$ erg. We obtained $P_{rot} = (2.848 \pm 0.001)$ days, and we found no evidence of differential rotation. We also found that this young active star presents a long-term activity cycle with a length of $\text{about four}$ years; there is less significant evidence of a shorter cycle of $0.8$ year. The star also shows a broad activity minimum between 1998 and 2004. We found a correlation between the S index, on the one hand, and the H$\alpha$ the Na I D indexes, on the other hand, although the saturation level of these last two indexes is not observed in the Ca lines. Because the maximum-entropy spot model does not reflect migration between active longitudes, this activity cycle cannot be explained by a solar-type dynamo. It is probably caused by an $\alpha^2$-dynamo.STAMPAenArticle10.1051/0004-6361/2020391642-s2.0-85097009386000595814100002https://www.aanda.org/articles/aa/abs/2020/12/aa39164-20/aa39164-20.htmlhttps://ui.adsabs.harvard.edu/abs/2020A%26A...644A...2I/abstractFIS/05 - ASTRONOMIA E ASTROFISICAERC sectors::Physical Sciences and Engineering::PE9 Universe sciences: astro-physics/chemistry/biology; solar systems; stellar, galactic and extragalactic astronomy, planetary systems, cosmology, space science, instrumentation::PE9_6 Stars and stellar systems