Relation between kneading matrices of a map and its iterates
Commun. Korean Math. Soc. 2020 Vol. 35, No. 2, 571-589
https://doi.org/10.4134/CKMS.c190255
Published online April 6, 2020
Chaitanya Gopalakrishna, Murugan Veerapazham
National Institute of Technology Karnataka Surathkal; National Institute of Technology Karnataka Surathkal
Abstract : 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.
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