Closed periodic orbits of convective solutions in rapidly rotating system: Double torus knots and links, DTK

The classification of closed periodic orbits of convection in a rapidly rotating system is given. It is shown that double torus knots and links, DTK, do occur, which is a very wide and important class of knots and links. We also proved that there is no double torus Lorenz knots, this answers question 6 raised by Hill and Murasugi in [Peter Hill, On double-torus knots 1. J Knot Theor Ramif 1999;8(8):1009–48]. It is also shown that the system produces torus knots and links, for some specific parameters. In fact this approach suggests the study of double torus knots and links through dynamical tools, such as symbolic dynamics and templates.