Journal of Knot Theory and its Ramifications , Volume 16 - Issue 4 p. 97- 114
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|
|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)|
|Journal of Knot Theory and its Ramifications|
|Computational Topology for Systems and Control|
Collins, P.J. (2007). Universal Trellises. Journal of Knot Theory and its Ramifications, 16(4), 97–114.