Is it possible to predict whether it will rain tomorrow or next week? The simple answer is no. Despite the precision of measurements, the anticipated behavior can significantly deviate from reality. This unpredictability, often referred to as chaos, precludes the quantitative prediction of a system’s evolution. Consequently, we turn to qualitative explanations, such as estimating the average number of rainy days in a year. My research delves into this qualitative perspective, examining non-uniformly hyperbolic models that display asymptotic contraction and expansion. These models are highly versatile, finding applications in diverse fields ranging from biology to sociology. To comprehend these models, I employ symbolic dynamics. By altering coordinates, we can substitute trajectories with sequences of symbols. This transformation simplifies the study of qualitative properties and aids in detecting the presence of chaos in nature.