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We have undertaken a thorough dynamical investigation of five extrasolarplanetary systems using extensive numerical experiments. The systems Gl 777 A,HD 72659, Gl 614, 47 Uma and HD 4208 were examined concerning the question ofwhether they could host terrestrial like planets in their habitable zones(=HZ). First we investigated the mean motion resonances between fictitiousterrestrial planets and the existing gas giants in these five extrasolarsystems. Then a fine grid of initial conditions for a potential terrestrialplanet within the HZ was chosen for each system, from which the stability oforbits was then assessed by direct integrations over a time interval of 1million years. The computations were carried out using a Lie-series integrationmethod with an adaptive step size control. This integration method achievesmachine precision accuracy in a highly efficient and robust way, requiring nospecial adjustments when the orbits have large eccentricities. The stability oforbits was examined with a determination of the Renyi entropy, estimated fromrecurrence plots, and with a more straight forward method based on the maximumeccentricity achieved by the planet over the 1 million year integration.Additionally, the eccentricity is an indication of the habitability of aterrestrial planet in the HZ; any value of e>0.2 produces a significanttemperature difference on a planet's surface between apoapse and periapse. Theresults for possible stable orbits for terrestrial planets in habitable zonesfor the five systems are summarized as follows: for Gl 777 A nearly the entireHZ is stable, for 47 Uma, HD 72659 and HD 4208 terrestrial planets can survivefor a sufficiently long time, while for Gl 614 our results exclude terrestrialplanets moving in stable orbits within the HZ.Comment: 14 pages, 18 figures submitted to A&

Stability of terrestrial planets in the habitable zone of Gl 777 A, HD 72659, Gl 614, 47 Uma and HD 4208