Topological chaos and periodic braiding of almost-cyclic sets,
Physical Review Letters 106, 114101. [2011]

Mark A. Stremler, Shane D. Ross, Piyush Grover, Pankaj Kumar
Engineering Science and Mechanics, Virginia Tech


In certain (2+1)-dimensional dynamical systems, the braiding of periodic orbits provides a framework for analyzing chaos in the system through application of the Thurston-Nielsen classification theorem. Periodic orbits generated by the dynamics can behave as physical obstructions that 'stir' the surrounding domain and serve as the basis for this topological analysis. We provide evidence that, even in the absence of periodic orbits, almost-cyclic regions identified using a transfer operator approach can reveal underlying structure that enables topological analysis of chaos in the domain.

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