The Lorenz equations are quadratic, and already have an infinite number of distinct knotted and linked orbits. An answer to one of your other questions has good references on Lorenz orbits, but I also like this nice set of slides from Joan Birman. Relevant to this question, torus knots / links of all types appear as orbits. This means you can get arbitrarily high linking numbers with a degree-two polynomial vector field.

The Lorenz equations are quadratic, and already have an infinite number of distinct knotted and linked orbits. An answer to one of your other questions has good references on Lorenz orbits, but I also like this nice set of slides from Joan Birman. To be concrete, torus knots / links of all types appear as orbits. This means you can get arbitrarily high linking numbers with a degree-two polynomial vector field.

The Lorenz equations are quadratic, but already have an infinite number of distinct knotted and linked orbits. An answer to one of your other questions has good references on this, but I also like this nice set of slides from Joan Birman. Relevant to this question, torus knots / links of all types appear as orbits. This means you can get arbitrarily high linking numbers with a degree-two polynomial vector field.

The Lorenz equations are quadratic, and already have an infinite number of distinct knotted and linked orbits. An answer to one of your other questions has good references on Lorenz orbits, but I also like this nice set of slides from Joan Birman. Relevant to this question, torus knots / links of all types appear as orbits. This means you can get arbitrarily high linking numbers with a degree-two polynomial vector field.