Coexistence of hyperbolic and elliptic invariant tori for completely degenerate quasi-periodically forced maps
Coexistence of hyperbolic and elliptic invariant tori for completely degenerate quasi-periodically forced maps
Consider the following completely degenerate quasi-periodically forced skew-product maps of the form \begin{document}$ \begin{eqnarray*} \left\{ \begin{array}{l} \bar{x} = x+y^m+\epsilon f_1(x,y,\theta,\epsilon)+h_1(x,y,\theta,\epsilon),\\ \bar{y} = y+ \lambda x^n+\epsilon f_2(x,y,\theta,\epsilon)+h_2(x,y,\theta,\epsilon),\\ \bar{\theta} = \theta+\omega, \end{array} \right. \end{eqnarray*} $\end{document} where $ (x,y,\theta)\in \mathbb{R}\times\mathbb{R}\times \mathbb{T}^d $, $ \lambda = \pm 1 $, $ \omega\in\mathbb{R}^d, $ $ n …