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Rigidity and global deformations in dynamics

Final Report Summary - RGDD (Rigidity and global deformations in dynamics)

One of the main tools in science is to take repeated measurements of objects that are assumed to depend on time via
some (essentially) deterministic evolution. It turns out that in some deterministic systems such time averages do not exist:
such systems do not have a stationary invariant measure, and the time average can fluctuate over time. This project developed techniques which should make it possible to show that for most one-dimensional systems such time averages do indeed exist.

The project also considered networks of coupled one-dimensional systems. It was shown that provided that the network
is rather heterogeneous (so some nodes have many more connections than others) one can apply ergodic averaging techniques. This made it possible to explain why one observes layered dynamics in such systems: at some nodes one has quite different dynamics than at other notes.