ERGODICNONCOMPACT · Ergodic theory on non compact spaces

The proposal is to look for, and investigate, new ergodic theoretic types of behavior for dynamical systems which act on non compact spaces. These could include transience and non-trivial ways of escape to infinity, critical phenomena similar to phase transitions, and new types of measure rigidity. There are potential applications to smooth ergodic theory (non-uniform hyperbolicity), algebraic ergodic theory (actions on homogeneous spaces), and probability theory (weakly dependent stochastic processes).