Energy-dependent periodicities of LS I +61$^\circ$ 303 in the GeV band

LS I +61$^\circ$303 is a rare representative of the gamma-ray binaries with a compact object known to be a pulsar. We report on the periodicity and spectral analysis of this source performed with more than 14 years of Fermi/LAT data. The periodicity of LS I +61$^\circ$303 is strongly energy dependent. Two periods $P_1 = 26.932\pm 0.004 (stat)\pm 0.008 (syst)$ and $P_2 = 26.485 \pm 0.004 (stat)\pm 0.007 (syst)$ are detected only at $E>1$ GeV and at $E<0.3$ GeV correspondingly. Within $1\sigma$ (stat+syst) the periods are consistent with orbital ($P_2$) and beat orbital/superorbital ($P_1$) periods. We present the orbital light curves of the system in several energy bands and the results of the spectral analysis. We discuss the possible origin of the change in the variability pattern between 0.1 and 1 GeV energy.