TITLE: Chaos and quasi-periodicity in diffeomorphisms of the solid torus AUTHORS: Henk W. Broer^(1), Carles Sim\'o^(2) and Renato Vitolo^(3) \begin{document} (1) Dept. of Mathematics, University of Groningen, Blauwborgje 3, 9747 AC Groningen, The Netherlands (2) Dept. de Matem\`atica Aplicada i An\`alisi, Universitat de Barcelona, Gran Via, 585, 08007 Barcelona, Spain (3) Dip. di Mat. e Informatica, Universit\`a di Camerino, via Madonna delle Carceri, 62032 Camerino, Italy E-mail: broer@math.rug.nl, carles@maia.ub.es, renato.vitolo@unicam.it ABSTRACT: The H\'enon family of planar maps is considered driven by the Arnol'd family of circle maps. This leads to a five-parameter family of skew product systems on the solid torus. In this paper the dynamics of this skew product family and its perturbations are studied. It is shown that, in certain parameter domains, H\'enon-like strange attractors occur. The existence of quasi-periodic H\'enon-like attractors is partially discussed, and further supported by numerical evidence.