Can there be an Earth-like planet in HD37605?

Abstract: Detection of Earth-mass planets on orbits around 1 AU with the radial velocity method has so far not been possible, the Doppler velocity they induce on their host star is too small to be detected. Planetary systems detected with the radial velocity method might then contain undetected Earth-like planets. One such planetary system is HD37605, which contains a star similar to the Sun and two gas giants. One on a highly eccentric low semi-major axis orbit, and one on a near circular orbit almost 4 AU out. In this thesis the possibility that an Earth-like planet, with 1 M$_\oplus$ or 2 M$_\oplus$ masses, can remain on stable orbits within the habitable zone of HD37605 is investigated. This is done by simulating HD37605 with an additional planet for 20 Myr using the Mercury package. Orbits are considered stable if the simulations does not end in an ejection or collision, and they are considered habitable if the additional planet never leaves the habitable zone. It was found that stability varies a lot over the habitable zone. Peak stability occurs at 0.9 AU and 1.2 AU, and peak instability at 1.1 AU. Habitable runs were found in a region between 0.95 AU and 1 AU. This was the only region where the eccentricity oscillations induced on the additional planet can remain small enough that the planet does not leave the habitable zone.