Choosing roots of polynomials with symmetries smoothly
英文摘要：
The roots of a smooth curve of hyperbolic polynomials may not in general be parameterized smoothly, even not $C^{1,α}$ for any $α> 0$. A sufficient condition for the existence of a smooth parameterization is that no two of the increasingly ordered continuous roots meet of infinite order. We give refined sufficient conditions for smooth solvability if the polynomials have certain symmetries. In general a $C^{3n}$ curve of hyperbolic polynomials of degree $n$ admits twice differentiable parameterizations of its roots. If the polynomials have certain symmetries we are able to weaken the assumptions in that statement.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
