Blenders for a non-normally Henon-like family (Q2786395)

The family of real polynomials on~\(\mathbb R^3\), given by \(\varphi(x,y,z)=(1-ax^2+by,x,cz+dx)\), with \(a,b,c,d\) such that \(|c|>1\), is addressed to as a ``non-normally Hénon-like family'' (for \(c=d=0\) it is the standard Hénon family). A blender is a certain hyperbolic structure which can very roughly be described as an invariant set with a uniformly hyperbolic splitting. The main result gives conditions on the parameters \(a,b,c,d\) to have a non-normal hyperbolic horseshoe containing a saddle fixed point for \(d=0\), and to have a blender containing a saddle fixed point with a two-dimensional stable segment inside the blender for \(d\neq0\).