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Figure 1: Fractional errors on the total energy E with respect to the initial one E0 (black curve), and on the total angular momentum H with respect to the initial one H0 (grey curve), as a function of time over the 108 yr integration. |
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Figure 2:
The 104 first years of the integration of the nominal
solution. The upper plots show the temporal evolution of the
eccentricity of the three planets Gl 581 b), c), and d), from left to right,
respectively; the lower plots are the same for the longitude of
periastron ![]() |
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Figure 3:
Stability of the three-planet system in various
configurations. The maximum variation range for the semi-major
axes ( upper plots) and for the eccentricities ( lower plots) is displayed
as a function of the assumed viewing inclination of the system with respect
to pole-on. Each cross corresponds to a single simulation. The left
plots correspond to simulations with the nominal eccentricities as
initial conditions, and the right plots to simulations with
eccentricities increased by ![]() |
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Figure 4: Progress of the calculation of the partial Lyapunov exponents as a function of the integration time, in the nominal case for Gl 581 (zero inclination, nominal eccentricities). At t=104 yr, the three exponents have stabilised. |
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Figure 5:
Lyapunov exponents as a function of the
inclination i, computed for all the simulations described in
Fig. 3. Left plot: simulations with nominal
eccentricities; Right plot: simulations with ![]() |
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