Basin Properties in Two-Dimensional Noninvertible Maps

Abstract

Properties of the basins of noninvertible maps of the plane are studied using the method of critical curves. The paper considers the class of maps having a region of the phase plane where the number of first rank preimages is greater than two. More particularly, the paper gives the conditions of existence of a connected basin, a nonconnected basin and a multiply connected basin in maps where the segments of the critical curve separate the plane into regions, one with three first rank preimages and the other with only one preimage. Then, maps having a maximum number of first rank preimages equal to four are considered.