The annulus principle in the existence problem for a hyperbolic strange attractor (Q2817560)

The authors consider an ``annulus'' as the cartesian product of a ball in \(\mathbb{R}^k\), \(k\geq 2\), and a circle. They investigate the diffeomorphism \(\Pi\) of an annulus defined as \((v, \varphi)\mapsto (f(v,\varphi), m\varphi + g(v,\varphi)\pmod {2\pi})\), where \(m\) is a integer such that \(|m| \geq 2 \), and \(f, g\) are differentiable functions \(2 \pi\)-periodic in the second coordinate.NEWLINENEWLINEThe authors give sufficient conditions on the functions \(f\) and \(g\) so that the diffeomorphism \(\Pi\) has a hyperbolic strange attractor of Smale-Williams solenoid-type in the annulus. More specifically, the authors assume conditions on the partial derivatives of \(\Pi\) and prove that the maximal attractor of \(\Pi\) is a hyperbolic set, a solenoid and it is topologically mixing.