"When Topology forces Dynamics"Boyland, PhilipWe describe various situations where topological phenomenon like the structure of a base space or the action on $\pi_1$ or $H_1$ force dynamical complexity. These results often take the form of a stability theorem: there is a model system with well-understood, complicated dynamics and one proves that these dynamics persist under large perturbations as long as one stays on the same manifold or in the same homotopy class. We give various dynamical applications of these results such as invariant decompositions and an analog of Sharkovskii's theorem for surface dynamics as well as physical applications to fluid mixing and Hamiltonian dynamics on hyperbolic manifolds. |
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