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Detection of Earth-mass planets with the radial velocity method requires a precision of about 10cm/s to identify a signal caused by such a planet. At the same time, noise originating in the photospheric and subphotospheric layers of the parent star is of the order of meters per second. Understanding the physical nature of the photospheric noise (so-called stellar jitter) and characterizing it are critical for developing techniques to filter out these unwanted signals. We take advantage of current computational and technological capabilities to create 3D realistic models of stellar subsurface convection and atmospheres to characterize the photospheric jitter. We present 3D radiative hydrodynamic models of several solar-type target stars of various masses and metallicities, discuss how the turbulent surface dynamics and spectral line characteristics depend on stellar properties, and provide stellar jitter estimates for these stars.

We investigate the evolution of the rotational axes of exoplanets under the action of gravitational and magnetic perturbations. The planet is assumed to be dynamically symmetrical and to be magnetised along its dynamical-symmetry axis. By qualitative methods of the bifurcation theory of multiparametric PDEs, we have derived a gallery of 69 phase portraits. The portraits illustrate evolutionary trajectories of the angular momentum \({\vec L}\) of a planet for a variety of the initial conditions, for different values of the ratio between parameters describing gravitational and magnetic perturbations, and for different rates of the orbital evolution. We provide examples of the phase portraits, that reveal the differences in topology and the evolutionary track of \({\vec L}\) in the vicinity of an equilibrium state. We determine the bifurcation properties, i.e., the way of reorganisation of phase trajectories in the vicinities of equilibria; and we point out the combinations of parameters’ values that permit ip-overs from a prograde to a retrograde spin mode.

Assuming that the observed periodic variations of pulsar emission are due to the free precession of the spin axis, we investigate the evolution of the rotation of a two-layer neutron star using the Hamiltonian method of Getino. We model the dynamical characteristics of a rotating neutron star using the observed variations of the emission of seven pulsars. We estimate the dependence of the period of the Chandler wobble, the period of precession of the spin axis, and the dynamical ellipticity of a neutron star on the model used to describe the super-dense neutron matter and the mass of the star.

We investigate the equation describing the evolution of the kinetic momentum vector for the case of non-resonance rotation of dynamically symmetrical planets by action of gravitational and magnetic interaction with the central star. The obtained gallery of more twenty phase portraits of kinetic momentum evolution illustrates the various regimes of the planetary systems evolution. The analyses of obtained portraits has shown that a direct rotation of the planet may be passed into reverse rotation and vice versa for a rather broad range of the parameters.

For the plane motion we are completely analyzing the differential equations systems of gravitational capture of the exoplanet at the resonance rotation with action of gravitational and tidal torques by qualitative analysis and bifurcation theory of dynamical systems (DS). The separation of 3-dimensional parameter space of dynamical system by bifurcation surfaces is obtained. The gallery of more than thirty phase portraits of gravitational capture extends the known scenario of cosmogonical evolution of the exoplanet on the early time, when the tidal interaction is very important.

In this report, we present results of analytical and numerical calculations of evolution the axis of rotation of planets moving at very close orbits. We consider the evolution of the axis of rotation caused by tidal perturbations of a parent star and obtain estimates of the principal moment of inertia and the dynamical flattening for nine exoplanets. From analysis of evolutionary equations, we obtain the critical values of the kinetic momentum vector, $\vec L$, for different values of orbital eccentricity. We find a general tendency of vector $\vec L$ to evolve to the direction perpendicular to the orbital plane.

Extending the theory of core-mantle differential rotation of a planet, we have obtained the periods PCW and PFCN for different pulsars in the second approximation. We have investigated the dependence of these periods on the equation of state of neutron liquid, flatness of mantle and crust of the neutron star.

At present time there are investigations of precession and nutation for very different celestial multi-layer bodies: the Earth (Getino 1995), Moon (Gusev 2010), planets of Solar system (Gusev 2010) and pulsars (Link et al. 2007). The long-periodic precession phenomenon was detected for few pulsars: PSR B1828-11, PSR B1557-50, PSR 2217+47, PSR 0531+21, PSR B0833-45, and PSR B1642-03. Stairs, Lyne & Shemar (2000) have found that the arrival-time residuals from PSR B1828-11 vary periodically with a different periods. According to our model, the neutron star has the rigid crust (RC), the fluid outer core (FOC) and the solid inner core (SIC). The model explains generation of four modes in the rotation of the pulsar: two modes of Chandler wobble (CW, ICW) and two modes connecting with free core nutation (FCN, FICN) (Gusev & Kitiashvili 2008). We are propose the explanation for all harmonics of Time of Arrival (TOA) pulses variations as precession of a neutron star owing to differential rotation of RC, FOC and crystal SIC of the pulsar PSR B1828-11: 250, 500, 1000 days. We used canonical method for interpretation TOA variations by Chandler Wobble (CW) and Free Core Nutation (FCN) of pulsar.The two - layer model can explain occurrence twin additional fashions in rotation pole motion of a NS: CW and FCN. In the frame of the three-layer model we investigate the free rotation of dynamically-symmetrical PSR by Hamilton methods. Correctly extending theory of SIC-FOC-RC differential rotation for neutron star, we investigated dependence CW, ICW, FCN and FICN periods from flatness of different layers of pulsar.Our investigation showed that interaction between rigid crust, RIC and LOC can be characterized by four modes of periodic variations of rotation pole: CW, retrograde Free Core Nutation (FCN), prograde Free Inner Core Nutation (FICN) and Inner Core Wobble (ICW). In the frame of the three-layer model we proposed the explanation for all pulse fluctuations by differential rotation crust, outer core and inner core of the neutron star and received estimations of dynamical flattening of the pulsar inner and outer cores, including the heat dissipation. We have offered the realistic model of the dynamical pulsar structure and two explanations of the feature of flattened of the crust, the outer core and the inner core of the pulsar.