Parabolic function

From Diffgeom
Jump to: navigation, search


Let (m_1,m_2,\ldots,m_r) be a tuple of integers whose sum is n. Then, a function f:\R^n \to \R^n is said to be of parabolic type (m_1,m_2,\ldots,m_r) if for any k \le r, the effect on the first m_1 + m_2 \ldots m_k coordinates is independent of the values of the remaining coordinates.

If f is also continuously differentiable, this is equivalent to the condition that the Jacobian matrix of f be of parabolic type (m_!,m_2,\ldots,m_r).