Communications of the
Korean Mathematical Society CKMS

It is known that the kneading matrix associated with a continuous piecewise monotone self-map of an interval contains crucial combinatorial information of the map and all its iterates, however for every iterate of such a map we can associate its kneading matrix. In this paper, we describe the relation between kneading matrices of maps and their iterates for a family of chaotic maps. We also give a new definition for the kneading matrix and describe the relationship between the corresponding determinant and the usual kneading determinant of such maps.

Keywords: Dynamical system, piecewise monotone map, kneading matrix, kneading determinant

MSC numbers: Primary 37E05; Secondary 15A24

Supported by: The second author was supported by the Science and Engineering Research Board
(SERB), DST, Government of India, through the project ECR=2017=000765.