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Abstract
We investigate differential invariants for homoclinic tangencies and discuss the role of these invariants in the Hausdorff dimension of invariant sets associated with the tangency and its unfoldings. Further, we give a streamlined proof of a theorem of Goncheko and Shilnikov on the case of a tangency in an area preserving map. Specifically, the invariants determine whether or not a hyperbolic invariant set is formed near the tangency.
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