  The existing results about inversion of a tippe top (TT) establish stability
of asymptotic solutions and prove inversion by using the LaSalle theorem.
Dynamical behaviour of inverting solutions has only been explored numerically
and with the use of certain perturbation techniques. The aim of this paper is
to provide analytical arguments showing oscillatory behaviour of TT through the
use of the main equation for the TT. The main equation describes time evolution
of the inclination angle $\theta(t)$ within an effective potential
$V(\cos\theta,D(t),\lambda)$ that is deforming during the inversion. We prove
here that $V(\cos\theta,D(t),\lambda)$ has only one minimum which (if Jellett's
integral is above a threshold value
$\lambda>\lambda_{\text{thres}}=\frac{\sqrt{mgR^3I_3\alpha}(1+\alpha)^2}{\sqrt{1+\alpha-\gamma}}$
and $1-\alpha^2<\gamma=\frac{I_1}{I_3}<1$ holds) moves during the inversion
from a neighbourhood of $\theta=0$ to a neighbourhood of $\theta=\pi$. This
allows us to conclude that $\theta(t)$ is an oscillatory function. Estimates
for a maximal value of the oscillation period of $\theta(t)$ are given.
