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INVARIANCE OF KNEADING MATRIX UNDER CONJUGACY

  • Gopalakrishna, Chaitanya (Department of Mathematical and Computational Sciences National Institute of Technology Karnataka Surathkal) ;
  • Veerapazham, Murugan (Department of Mathematical and Computational Sciences National Institute of Technology Karnataka Surathkal)
  • Received : 2019.05.30
  • Accepted : 2021.01.15
  • Published : 2021.03.01

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.