Normal form reduction for multiple-zero eigenvalue using fractional scales
In this paper, we present a new method for finding normal form equation and invariant manifold in the case of multiple zero eigenvalue with a single Jordan block. The method utilizes the concept of fractional scale. This allows using a single scale parameter in the normal form reduction for systems with multiple variables and parameters. The use of fractional scales substantially simplifies the procedure of system reduction. As an example, we perform the normal form reduction near the point of triple zero bifurcation for a double pendulum under a follower force.