  We have undertaken a thorough dynamical investigation of five extrasolar
planetary systems using extensive numerical experiments. The systems Gl 777 A,
HD 72659, Gl 614, 47 Uma and HD 4208 were examined concerning the question of
whether they could host terrestrial like planets in their habitable zones
(=HZ). First we investigated the mean motion resonances between fictitious
terrestrial planets and the existing gas giants in these five extrasolar
systems. Then a fine grid of initial conditions for a potential terrestrial
planet within the HZ was chosen for each system, from which the stability of
orbits was then assessed by direct integrations over a time interval of 1
million years. The computations were carried out using a Lie-series integration
method with an adaptive step size control. This integration method achieves
machine precision accuracy in a highly efficient and robust way, requiring no
special adjustments when the orbits have large eccentricities. The stability of
orbits was examined with a determination of the Renyi entropy, estimated from
recurrence plots, and with a more straight forward method based on the maximum
eccentricity achieved by the planet over the 1 million year integration.
Additionally, the eccentricity is an indication of the habitability of a
terrestrial planet in the HZ; any value of e>0.2 produces a significant
temperature difference on a planet's surface between apoapse and periapse. The
results for possible stable orbits for terrestrial planets in habitable zones
for the five systems are summarized as follows: for Gl 777 A nearly the entire
HZ is stable, for 47 Uma, HD 72659 and HD 4208 terrestrial planets can survive
for a sufficiently long time, while for Gl 614 our results exclude terrestrial
planets moving in stable orbits within the HZ.
