Abstract: In 1970s S.Newhouse discovered that a generic homoclinic bifurcation of a smooth surface diffeomorphism leads to persistent homoclinic tangencies, infinite number of attractors (or repellers), and other unexpected dynamical properties (nowadays called “Newhouse phenomena”). More than 20 years later P.Duarte provided an analog of these results in conservative setting (with attractors replaced by elliptic periodic points). We use his techniques to show that a two-dimensional conser- vative homoclinic bifurcation also give birth to hyperbolic sets of large Hausdorff dimension. Applications related to the standard map and celestial mechanics (this is a joint project with V.Kaloshin) will be discussed.