Aims. The aim of this paper is to analyse the previously discovered
discontinuity of the periodicity of the GeV γ-ray emission of the
radio-loud X-ray binary LS I +61{\deg}303 and to determine its physical origin.
Methods. We used wavelet analysis to explore the temporal development of
periodic signals. The wavelet analysis was first applied to the whole data set
of available Fermi-LAT data and then to the two subsets of orbital phase
intervals Φ=0.0−0.5 and Φ=0.5−1.0. We also performed a
Lomb-Scargle timing Analysis. We investigated the similarities between GeV
γ-ray emission and radio emission by comparing the folded curves of the
Fermi-LAT data and the Green Bank Interferometer radio data. Results. During
the epochs when the timing analysis fails to determine the orbital periodicity,
the periodicity is present in the two orbital phase intervals Φ=0.0−0.5 and Φ=0.5−1.0. That is, there are two periodical signals, one
towards periastron (i.e., Φ=0.0−0.5) and another one towards apoastron
(Φ=0.5−1.0). The apoastron peak seems to be affected by the same
orbital shift as the radio outbursts and, in addition, reveals the same two
periods P1​ and P2​ that are present in the radio data. Conclusions. The
γ-ray emission of the apoastron peak normally just broadens the emission
of the peak around periastron. Only when it appears at Φ≈0.8−1.0, because of the orbital shift, it is enough detached from the first peak
to become recognisable as a second orbital peak, which is the reason why the
timing analysis fails. Two γ-ray peaks along the orbit are predicted by
the two-peak accretion model for an eccentric orbit, that was proposed by
several authors for LS I +61{\deg}303.Comment: 7 pages, 4 figures, A&A (2014