Holomorphic shadowing for Henon maps
by
Phil Mummert
Taylor University, Upland, Indiana

Sterling and Meiss introduced anti-integrable limits in the setting of real Henon maps. By extending these ideas, we describe a correcting operator for those pseudo-orbits of the quadratic complex Henon map that remain bounded away from the origin by an amount that depends on the map. The iterates of this correcting operator converge to a holomorphic motion that respects the dynamics. This computational procedure (shadowing) can be applied in the context of horseshoes and solenoids and leads to an algorithm for finding the Julia set in certain cases.

Date received: February 25, 2008