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Zeros of the kneading invariant and topological entropy for Lorenz maps

机译:Zeros of the kneading invariant and topological entropy for Lorenz maps

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摘要

Ifis a unimodal map, then its topological entropy is related to the smallest positive zero s of a certain power series (the kneading invariant of f) by. Moreover, it is implicit in the results of Jonker and Rand that for each positive entropy basic setin the renormalization decomposition of the non-wandering set of f, there is a real zeroof the kneading invariant such that. Here we prove a similar result for Lorenz maps. In contrast to the unimodal case, it is possible for two basic sets in the renormalization decomposition of the non-wandering set of a Lorenz map to have the same entropy, and we show that in this case there is a corresponding double zero of the kneading invariant.

著录项

  • 来源
    《nonlinearity》 |1996年第4期|999-1014|共页
  • 作者

    Paul Glendinning; Toby Hall;

  • 作者单位

    DAMTP, Silver Street, Cambridge CB3 9EW, UK;

    Centre de Recerca Matemàtica, Institut d'Estudis Catalans, Apartat 50, E-08193 Bellaterra, Spain;

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  • 正文语种 英语
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