The main goal in this paper was to provide a novel chaos indicator based on a topological model which allows to calculate the fractal dimension of any curve. A fractal structure is a topological tool whose recursiveness becomes ideal to generalize the concept of fractal dimension. In this paper, we provide an algorithm to calculate a new fractal dimension specially designed for a parametrization of a curve or a random process, whose definition is made by means of fractal structures. As an application, we explore the use of this new concept of fractal dimension as a chaos indicator for dynamical systems, in a similar way to the classical maximal Lyapunov exponent. To illustrate it, we apply the new fractal dimension as an indicator to model the chaotic behavior of a satellite which is moving around a planet whose gravity field is approximated by the field of a point mass.

Information theory is a useful framework of research that has been recently adapted to be used in the field of cognitive workload study for pilot performance. Mental workload assessment and forecasting modelling outputs based on Shannon’s Law have showed up as relevant feedback for managers with responsibilities in designing and optimizing the learning procedures involved. Therefore, the aim of this article is to apply this methodology to propose a mental workload baseline, caused by listening practice in English as a foreign language for a dual educational system (Military-STEM) where students must achieve an Industrial Engineering degree simultaneously with Military Pilot studies distributed in a four-year term program. For such purpose, it is summarised a case of study where the Mental Workload Assessment-Information Theory (MWA-IT) and the NASA Task Load Index (NASA-TLX), as one of the most cited references on workload studies, have been used to propose a reference baseline of expected workload. The paper introduces first a review regarding English as a foreign language in academic background, the workload methodologies mentioned before and the case of study characterization that set the database used. Applying MINITAB software for statistical analysis it is concluded finally that the nondimensional workload reference baseline was, for MWA-IT within 36.5 to 92.6 meanwhile NASA-TLX was within 49.8 to 193.7, and also that almost 65% of the workload due English Listening proficiency achievement was caused along the first two courses, when advanced STEM subjects are taught and before the elementary pilot learning and practice program starts.