Flows with knotted closed orbits (Q2776338)

The most outstanding feature of a flow in 3-space is its set of closed orbits, i.e., of the orbits homeomorphic to a circle. If finite in number they form a classical link. The present survey, describes the road to the extensive set of examples and their properties known today, on the basis of the historical development, and including many proofs. The principal building blocks, vertical flows in rectangular boxes, are pieced together by special affine maps. This can be represented by certain symbolic dynamics, and the so-called templates construct embeddings of the abstract flows in 3-space. The description of links using braids leads to the highlight among the results: the existence of flows containing all knots and links (key word ``universal template''). As pointed out, these even do occur in differential equations of electrical circuit theory. It is a pleasure to study this guide to the overlap of two concepts originally far apart: dynamical system and link.NEWLINENEWLINEFor the entire collection see [Zbl 0977.00029].