Existence of generic homoclinic tangencies for Hénon mappings
A computer-assisted rigorous proof is given of the following Theorem: The map \(H_{a,b}:\mathbb{R}^ 2\to\mathbb{R}^ 2\), \(H_{ab}(x,y)=(1-ax^ 2+by,x)\), has a generic homoclinic tangency for the one-parameter family \(H_{a,b}\) for some parameter \(a=1.3924198079\ldots\) and any fixed \(b\) close to 0.3. This parameter value for \(a\) is close to Hénon's original value of \(a=1.4\). The proof relies on complexification and estimates of the power series expansions of the stable and unstable manifolds.
scientific article; zbMATH DE number 118432
scientific article