Bifurcation from Landau solutions

Determine whether a non-Landau bifurcation exists from the family of Landau solutions, including whether the linearized operator around a Landau solution has kernel elements beyond the infinitesimal variations of the Landau parameters.

Background

The paper identifies bifurcation from a Landau solution as a sub-conjecture related to the broader rigidity conjecture. A bifurcation would correspond, at the linearized level, to an element of the kernel not generated by differentiating the Landau family with respect to its momentum parameters. The paper proves a classification of the self-similar kernel, but does not resolve the broader bifurcation question in the unrestricted or generally discretely self-similar setting.