The past few decades of dynamical systems theory have established that multiparameter nonlinear dynamical systems can exhibit extremely complex behavior with respect to both the system variables and parameters. Such complex behavior proven in theoretical work has to be contrasted with the capabilities of application; in the case of modeling multiscale processes, for instance, measurements may b...

A popular view in contemporary Boltzmannian statistical mechanics is to interpret the measures as typicality measures. In measuretheoretic dynamical systems theory measures can similarly be interpreted as typicality measures. However, a justification why these measures are a good choice of typicality measures is missing, and the paper attempts to fill this gap. The paper first argues that Pitow...

The dynamical hypothesis threatens computationalism and its commitment to mental representations: the continuous, reciprocally causative nature of cognition renders impossible such an analysis. Andy Clark and Rick Grush have suggested a hybrid approach that models cog-nitive systems using dynamical systems theory but employs mental representation via emulation to aid its explanations. I will ca...

In the last two decades, the mathematical analysis of material transport has received considerable interest in many scientific fields such as ocean dynamics and astrodynamics. In this contribution we focus on the numerical detection and approximation of transport barriers in dynamical systems. Starting from a set-oriented approximation of the dynamics we combine discrete concepts from graph the...

In recent years substantial progress, much of it resulting directly from ONR funding initiatives, has been made in understanding fundamental features of transport and mixing in oceans using methods derived from dynamical systems theory. The purpose of the current collaborative research is to extend these methods to the design of control algorithms for Drifter Motion Planning for Optimal Surveil...

The topological pressure of dynamical systems theory is examined from a computability theoretic point of view. It is shown that for sofic shift dynamical systems, the topological pressure is a computable function. This result is applied to a certain class of one dimensional spin systems in statistical physics. As a consequence, the specific free energy of these spin systems is computable. Final...

In this paper, we consider a planar dynamical system with a piecewise linear function containing an arbitrary number (but finite) of dropping sections and approximating some continuous nonlinear function. Studying all possible local and global bifurcations of its limit cycles, we prove that such a piecewise linear dynamical system with k dropping sections and 2k + 1 singular points can have at ...