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RELATION BETWEEN KNEADING MATRICES OF A MAP AND ITS ITERATES

  • Gopalakrishna, Chaitanya (Department of Mathematical and Computational Sciences National Institute of Technology Karnataka Suarthkal) ;
  • Veerapazham, Murugan (Department of Mathematical and Computational Sciences National Institute of Technology Karnataka Suarthkal)
  • Received : 2019.07.24
  • Accepted : 2019.11.19
  • Published : 2020.04.30

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

Acknowledgement

Supported by : Science and Engineering Research Board (SERB)

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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