The recent discovery of several exoplanets with probable terrestrial composition andlocated in unusual orbits very close to their respective stars leads to questions likedynamical stability including the rotational one. The dynamics of rotation has been studied currently by using classical models of rotation around the axis of larger momentof inertia, which is supposed perpendicular to the orbital plane (e.g. Callegari andRodriguez 2012). Such modelings are simplified since they do not consider inhomogeneities inthe interior of the planet, a hypothesis which must be considered in view ofstudies showing the possibility of interior differentiation of exoplanets (e.g.Madhusudhan et al. 2012). In this work we willstudy the dynamics of planetarydifferential rotation with the coupled differential equations of differents internal layers(e.g. Van Hoolst et al. 2008), extensively applied in the case of regular satellites of the solar system and terrestrialplanets. The models of differential rotationinclude the conservative mutual gravitational core-mantle effects. We first showindividual numerical simulations quantifying these coupling in the evolution of the physicallibration (mantle and core) in several initial configurations around the mainspin-orbit resonances, for different possible internal structures of Super-Earths.Then the dynamic of rotation is investigated in details through the construction ofdynamic maps based on the calculation of the spectral number associated to the amplitudes in the spectrum of the angle of rotation of the mantle. In addition tolarge sets of initial conditions, the effects of the core-mantle will bequantified considering also a wide interval of parameters like the density values of themantle and of the external and internal cores, and prolateness coefficients, all of themunknown in the case exoplanets. Different exoplanets will be studied, such as 55 Cnc e,CoRoT-7b, Kepler-9d and Kepler-10b. The planetary dynamics will be initially givenby the approximation of the two-body problem. For multi-planetary systems themutual gravitational interactions between the planets, and therefore the indirecteffects of a third body in the Super-Earth's rotation, will be investigated.
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