A map with invariant Cantor set of positive measure
Many examples exist of one-dimensional systems that are topologically conjugate to the shift operator on Σ2 and are thus chaotic. Most of these examples which have invariant Cantor subsets, have Cantor subsets of measure zero. In this paper we outline the formulation of a map on a closed interval that has an invariant Cantor subset of positive Lebesgue measure. We also survey techniques used to analyze the dynamics of one-dimensional systems.
Nonlinear Analysis, Theory, Methods and Applications
Murdock, J., & Botelho, F. (2005). A map with invariant Cantor set of positive measure. Nonlinear Analysis, Theory, Methods and Applications, 63 (5-7) https://doi.org/10.1016/j.na.2004.09.024