Cubic Maps as Models of Two-Dimensional Antimonotonicity

Chaos, Solitons & Fractals 1, 137 (1991)https://ireap.umd.edu/10.1016/0960-0779%2891%29900004-S1991Journal ArticleComplex and Emergent Systems

Families of dissipative two-dimensional diffeomorphisms that satisfy certain regularity conditions have been proved to be antimonotone [Kan et al., preprint (1990)], i.e. there are infinitely many periodic orbits created and infinitely many destroyed near certain parameter values of the system. We show that, in general, this sequence of creation and destruction of periodic orbits can also be modeled by families of one-dimensional maps with at least two critical points.