| While in the Harvard College Observatory he worked on many mathematical and astronomical subjects including topology and ergodic theory. |
| Armed with this understanding of the definition of ergodicity, we can now discuss some important properties of ergodic systems. |
| Here, there are various results demonstrating that strongly ergodic classical billiards, when quantized, exhibit quantum ergodicity. |
| In the stochastic case, we prove a multiplicative ergodic theorem, asserting that the stochastic spectral vector exists in all cases. |
| We have a long way to go before we understand the ergodic theory of strange attractors. |
| For the quadrant version, we prove the existence of temporally ergodic evolutions and of spatially ergodic ones. |
