Fabian Haiden studies connections among geometry, dynamical systems and category theory. His course notes Dynamics, Stability, and Noncommutative Algebra by Fabian Haiden develop topological entropy using covers and separated or spanning sets of trajectories, making orbit complexity into a quantitative invariant.
His research page connects these themes with stability conditions and categorical constructions. This illustrates how different mathematical descriptions can carry information about the same dynamics.[ref]

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