Boxing-in of a blender in a Hénon-like family

Introduction The extension of the Smale horseshoe construction for diffeomorphisms in plane to those spaces at least dimension three may result a hyperbolic invariant set referred as blender. defining property blender is that it has stable or unstable manifold appears have larger than expected. In this study, we consider Hénon-like family ℝ 3 , which only explicitly given example system known feature certain range parameter (corresponding an expansion contraction rate). More specifically, part its set, pair saddle fixed points with one-dimensional manifolds. When there blender, closure these manifolds cannot be avoided by curves coming from appropriate direction. This been checked method computing extremely long pieces global determine over exists. Methods take complimentary and local point view constructing actual three-dimensional box (a parallelopiped) acts outer cover set. successive forward backward images form nested sequence sub-boxes contains well respective manifold. Results constitutes that, contrast idealized affine construction, quite general features curved edges. initial defined parameter-dependent way, allows us characterize properties intuitively. Discussion particular, trace relevant edges function provide additional geometric insight into when not