Renormalization and conjugacy of piecewise linear Lorenz maps |
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Authors: | Hongfei Cui Yiming Ding |
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Affiliation: | Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, PR China |
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Abstract: | We investigate the uniform piecewise linearizing question for a family of Lorenz maps. Let f be a piecewise linear Lorenz map with different slopes and positive topological entropy, we show that f is conjugate to a linear mod one transformation and the conjugacy admits a dichotomy: it is either bi-Lipschitz or singular depending on whether f is renormalizable or not. f is renormalizable if and only if its rotation interval degenerates to be a rational point. Furthermore, if the endpoints are periodic points with the same rotation number, then the conjugacy is quasisymmetric. |
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Keywords: | 37E05 37F25 |
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