Abstract. The "escape windows" through which stars may escape from a galaxy are investigated by means of Poincaré sections of a simplified axi-symmetric model of the potential. The spiral shape of the windows are analyzed in details by constructing a normal form in the vicinity of an unstable periodic orbit.

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We focus on the updating of a specific contribution to the precession of the equator in longitude, usually named as "second order." It stems from the crossing of certain terms of the lunisolar gravitational potential. The IAU2006 precession theory assigns it the value of −46.8 mas/cy that was derived for a rigid Earth model. Instead of that model, we consider a two-layer Earth composed of an elastic mantle and a liquid core, working out the problem within the Hamiltonian framework developed by Getino and Ferrándiz. The targeted effect is obtained without further simplifying assumptions through Hori's canonical perturbation method applied up to the second order of perturbation. On account of using a more realistic Earth model, the revised value of the second-order contribution is significantly changed and reaches −55.29 mas/cy. That variation of the second-order contribution is larger than other contributions included in IAU2006. It must be compensated with an increase of −8.51 mas/cy in the value of the lunisolar first-order component ¢ p A of the precession of the equator rate, which is derived from the total rate by subtracting the remaining contributions accounted for in IAU2006 precession. The updating of the second-order contribution implies that the ¢ p A parameter has to be changed, from 5040684.593 to 5040693.104 mas/cy in absence of potential revisions of other contributions. It entails a proportional variation of Earth's dynamical ellipticity H d , for which the estimation associated with IAU2006, 0.00327379448, should be updated to 0.00327380001, about 1.7 ppm larger.

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