Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4665473 | Advances in Mathematics | 2015 | 38 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Hongfei Cui, Yiming Ding,