All Questions
3 questions
4
votes
3
answers
288
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A polynomial vector field on $\mathbb{R}^3$ which has a knot periodic orbit
Is there a polynomial vector field
$$P(x,y,z)\partial_x+Q(x,y,z)\partial_y+R(x,y,z)\partial_z$$
which has a closed orbit $K$ such that $K$ is a non trivial knot?
- 356
1
vote
0
answers
54
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Are total curvature and the unknoting number of closed orbits of algebraic vector fields bounded uniformly by the degree of vector field?
I am interested in this question since 1999 when I heared the definition of a knot and I read the definition of unknoting and the total curvature of a knot.
To what extent can closed ...
- 356
4
votes
0
answers
149
views
Connection between cardiac equations and untangling knots?
I was surprised to learn that there is (conjecturally) a connection between a cardiac muscle model known as the FitzHugh-Nagumo equations, and untangling knots:
Maucher, Fabian, and Paul Sutcliffe. ...
- 151k