  In this paper, we investigate whether hypothetical Earth-like planets have
high probability of remaining on stable orbits inside the habitable zones
around the stars A and B of {\alpha} Centauri, for lengths of time compatible
with the evolution of life. We introduce a stability criterion based on the
solution of the restricted three-body problem and apply it to the {\alpha}
Centauri system. In this way, we determine the regions of the short-term
stability of the satellite-type (S-type) planetary orbits, in both planar and
three-dimensional cases. We also study the long-term stability of hypothetical
planets through the dynamical mapping of the habitable zones of the stars. The
topology of the maps is analyzed using the semi-analytical secular Hamiltonian
model and possible processes responsible for long-lasting instabilities are
identified. We verify that the planetary motion inside the habitable zones is
regular, regardless of high eccentricities, for inclinations smaller than
40{\deg}. We show that the variation of the orbital distance of the planet
located in the habitable zones of the binary is comparable to that of Earth, if
the planet is close to the Mode I stationary solution. This result brings
positive expectations for finding habitable planets in binary stars.
