Abstract
For a class of piecewise linear maps on T on [0, 1] and \(0\le a<b\le 1\), we consider the invariant set \(T_{a,b}:=\bigcap \limits _{n=0}^{\infty }T^{-n}[a,b]\). We obtain a sufficient condition under which the Hausdorff dimension of the set \(T_{a,b}\) is locally constant.
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The work is supported by the National Natural Science Foundation of China, No. 11401445.
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Ding, Y., Hu, H., Yu, Y. (2015). On Hausdorff Dimension of Invariant Sets for a Class of Piecewise Linear Maps. In: Bohner, M., Ding, Y., Došlý, O. (eds) Difference Equations, Discrete Dynamical Systems and Applications. Springer Proceedings in Mathematics & Statistics, vol 150. Springer, Cham. https://doi.org/10.1007/978-3-319-24747-2_5
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DOI: https://doi.org/10.1007/978-3-319-24747-2_5
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