A flow in three-dimensions is universal if the periodic orbits contains all knots and links. Universal flows were shown to exist by Ghrist, and can be constructed by means of templates. Likewise, a planar diffeomorphism is universal if it has a suspension flow which is a universal flow. In this paper we prove the existence of a homoclinic trellis type for which any representative diffeomorphism is universal. This trellis type is remarkable in that it has zero entropy, and only two homoclinic intersection points.
universal template, homoclinic tangle, knot, trellis
SS中的纽结和连接(高维, 见57Q45) (msc 57M25), Homoclinic and heteroclinic orbits (msc 37C29), Fixed points, periodic points, fixed-point index theory (msc 37C25)
Life Sciences (theme 5), Energy (theme 4)
World Scientific
Journal of Knot Theory and its Ramifications
Computational Topology for Systems and Control
Scientific Computing

Collins, P.J. (2007). Universal Trellises. Journal of Knot Theory and its Ramifications, 16(4), 97–114.