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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