Journal of the
Korean Mathematical Society JKMS

In the kneading theory developed by Milnor and Thurston, it is proved that the kneading matrix and the kneading determinant associated with a continuous piecewise monotone map are invariant under orientation-preserving conjugacy. This paper considers the problem for orientation-reversing conjugacy and proves that the former is not an invariant while the latter is. It also presents applications of the result towards the computational complexity of kneading matrices and the classification of maps up to topological conjugacy.

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

MSC numbers: Primary 37E05, 37C15; Secondary 15A24

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