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There are some motivations to consider inflation driven by a phantom field. Before entering into some specific models and perform data fitting, it is important first investigating some general features that any viable inflation model should hold. The inflationary attractor property is an important one of those features. In this paper we will show that the inflationary attractor property still holds for canonical and Born-Infeld phantom fields in the standard Friedmann-Robertson-Walker cosmology, however, it does not hold for canonical and Born-Infeld phantom fields in the Randall -Sundrum II cosmology.

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