Invariance of kneading matrix under conjugacy
J. Korean Math. Soc. 2021 Vol. 58, No. 2, 265-281
Published online February 3, 2021
Printed March 1, 2021
Chaitanya Gopalakrishna, Murugan Veerapazham
National Institute of Technology Karnataka Surathkal; National Institute of Technology Karnataka Surathkal
Abstract : 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
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