Isotropization of scalar field Bianchi type-VII${}_h$ models with an exponential potential

We investigate the isotropization of the Bianchi type-VII${}_h$ cosmological models possessing a scalar field with an exponential potential of the form $V\left(\phi \right)=\Lambda e^{k\phi }$. In the case $k^2>2\mathrm{}$, we show that there is an open set of initial conditions in the set of anisotropic Bianchi type-VII${}_h$ initial data such that the corresponding cosmological models isotropize asymptotically. Hence scalar field spatially homogeneous cosmological models having an exponential potential with $k^2>2\mathrm{}$ can isotropize to the future.