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 an underlying structure that enables topological analysis of chaos in the domain.
Physical Review Letters
- Pub Date:
- March 2011
- Control of chaos applications of chaos;
- General topology;
- Laminar flows in cavities channels ducts and conduits;
- Chaos in fluid dynamics