Abstract
We survey some recently obtained generic consequences of the existence of homoclinic tangencies in diffeomorphisms of surfaces. Among other things, it has been shown that they give rise to invariant topologically transitive sets with maximal Hausdorff dimension, that they prohibit the existence of various kinds of symbolic extensions and that they form an impediment to the existence of Sinai–Ruelle–Bowen (SRB) measures. The main new result described here, together with a positive answer to an as yet unproved conjecture of Palis, would prove that generically on surfaces, SRB measures only exist on uniformly hyperbolic attractors.
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