TY - JOUR AB - We study generic unfoldings of homoclinic tangencies of two-dimensional area-preserving diffeomorphisms (conservative New house phenomena) and show that they give rise to invariant hyperbolic sets of arbitrarily large Hausdorff dimension. As applications, we discuss the size of the stochastic layer of a standard map and the Hausdorff dimension of invariant hyperbolic sets for certain restricted three-body problems. We avoid involved technical details and only concentrate on the ideas of the proof of the presented results. AU - Gorodetski, Anton AU - Kaloshin, Vadim ID - 8508 IS - 1 JF - Proceedings of the Steklov Institute of Mathematics KW - Mathematics (miscellaneous) SN - 0081-5438 TI - Conservative homoclinic bifurcations and some applications VL - 267 ER -