Cubic maps as models of two-dimensional antimonotonicity (Q1179425)

Families of dissipative two-dimensional \(C^ 3\) diffeomorphisms are known to have antimonotone parameter values [see \textit{I. Kan}, \textit{H. Koçak} and \textit{J. A. Yorke} ``Antimonotonicity: concurrent creation and annihilation of periodic orbits'' (preprint) (1990), see also \textit{I. Kan} and \textit{J. A. Yorke}, Bull. Am. Math. Soc., New Ser. 23, No. 2, 469-476 (1990; Zbl 0713.58026)]. This means that periodic orbits are created and also destroyed when one increases the parameter value monotonically in any neighbourhood of an antimonotone value. The authors show that families of one-dimensional maps with at least two critical points can also have antimonotone parameter values.