HÉNON MAP: SIMPLE SINKS GAINING COEXISTENCE AS b → 1

Abstract

The quadratic map of the interval displays one attractor for each parameter value. Conservative maps of the plane display infinite coexistence of stability islands around periodic orbits. Between these two extremes, dissipative systems of the plane are known to have infinite coexistence of sinks as a generic property, yet very hard to detect. We investigate how more and more coexistence is gained as the area-contraction rate b → 1. In this paper, we show a sequence of simple sinks gaining coexistence, and investigate the convergence properties of its bifurcation values. The sinks are simple, or primary, due to their geometrical structure.