A transformation of mappings preserving the property of robust chaos

Robust chaos is a phenomenon characterized by the continuous occurrence of chaos for the variability of control parameters. Therefore, chaotic systems with this property are highly desirable in various applications, e.g. chaos-based cryptography. One of the properties that allows the construction of maps with robust chaos is the S-unimodality property. This paper presents a new method to transform an S-unimodal map to its skew form while preserving the S-unimodal property. Thus, a new family of skew maps is defined with a new parameter $q\in (0,1)$, which allows the generation of robust chaos for any value of the parameter $q$. In addition to the theoretical results concerning this transformation, a number of examples of new families of chaotic maps are presented using known classical chaotic systems, such as the logistic map or the sine map. The application of skew maps in chaotic cryptography is also discussed in this paper.