| Contents |
| We study the first bifurcatoin problem of the real H\'enon map and show that the boundary of the full horseshoe locus is characterized by a tangency. This is a generalization of the result obtained by Bedford and Smillie for the parameter region with very small Jacobian. To extend their results, we need to develop several topological techniques and we also use rigorous interval arithmetic to verify the topological conditions on the configuration of stable and unstable manifolds of the map. We note that although the result itself is on the real H\'enon map, we need to work on the complex H\'enon map to obtain the proof, and therefore the invariant manifolds we need to control are complex curves. |
|