Julia sets of Newton maps of real quadratic polynomial maps on the plane

Abstract

We study numerically the $\alpha$- and $\omega$-limits of the Newton maps of two of the most elementary families of polynomial transformations on the plane: those with a linear component and those with both components of degree two. Our results are fully consistent with some conjectures we posed in a recent work about the dynamics of Newton maps.

42 pages, 16 figures

References in corpus (1)

• "Simple Dynamics" conjectures for some real Newton maps on the plane

Cited by in corpus (1)

• A Newton method for harmonic mappings in the plane