Stable sets of certain non-uniformly hyperbolic horseshoes have the expected dimension

Abstract

We show that the stable and unstable sets of non-uniformly hyperbolic horseshoes arising in some heteroclinic bifurcations of surface diffeomorphisms have the value conjectured in a previous work by the second and third authors of the present paper. Our results apply to first heteroclinic bifurcations associated to horseshoes with Hausdorff dimension $<22/21$ of conservative surface diffeomorphisms.

28 pages, 1 figure. Appendix A (by C. Matheus, C. G. Moreira and J. Palis) was added. Final version based on the referee report. To appear in J. Inst. Math. Jussieu