**"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. |