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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.
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참고문헌 (17)
참고문헌 신청
J. F. Alves / 1999 / Kneading Theory: A Functorial Approach / Communications in Mathematical Physics 204(1):89~114
J. F. ALVES / 1999 / Kneading theory for tree maps / Ergodic Theory and Dynamical Systems 24(4):957~985
Lori Alvin / 2011 / Adding machines, kneading maps, and endpoints / Topology and its Applications 158(3):542~550
Louis Block / 2012 / Semi-conjugacies and inverse limit spaces / Journal of Difference Equations and Applications 18(4):627~645
Acilina Caneco / 2009 / Kneading theory analysis of the Duffing equation / Chaos, Solitons & Fractals 42(3):1529~1538
J. F. ALVES / 1999 / Kneading theory for tree maps / Ergodic Theory and Dynamical Systems 24(4):957~985
Lori Alvin / 2011 / Adding machines, kneading maps, and endpoints / Topology and its Applications 158(3):542~550
Louis Block / 2012 / Semi-conjugacies and inverse limit spaces / Journal of Difference Equations and Applications 18(4):627~645
Acilina Caneco / 2009 / Kneading theory analysis of the Duffing equation / Chaos, Solitons & Fractals 42(3):1529~1538
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