Newton's method is a well-known iterative method to find roots of a function. The dynamics of the Newton maps of polynomials has long been an object of study, but far less is known about the Newton maps of rational functions. We determine which Newton maps of rational functions are conjugate to quadratic polynomials. We also prove that there are no Newton maps of rational functions which are conjugate to z3.
|Number of pages||20|
|Journal||Complex Variables and Elliptic Equations|
|State||Published - Oct 3 2019|
- Complex dynamics
- Newton map
- Yuri Antipov
- rational functions