Special curves and Hamiltonian systems from polynomial eigenfunctions of an elliptic operator

Abstract

A family of polynomials linked to the set of the deltoid tangents and its associated algebraic hypersurfaces has been presented in recent years. In this paper we study some related maximising and free plane curves. We also analyse the bifurcations on polynomial Hamiltonian dynamical systems defined from such a family.

arXiv comment14 pages, 7 figures