LDMRD Large Deviations and Measure Rigidity in Dynamics

Summary

The proposition aims to develop new tools in ergodic theory and dynamical systems, and explore applications to problems related to mathematical physics, geometry and arithmetics. The first general objective is to advance large deviation theory for non-compact dynamical systems. We plan to deduce new subexponential large deviation bounds for Gibbs measures on the countable Markov shift and explore how these results are linked to applications such as Pomeau-Manneville dynamics describing intermittence in the theory of turbulent flows, dynamical properties of the Gauss map, which is deeply connected to Diophantine approximation, and homogeneous dynamics such as the Teichmüller flow on translation surfaces. The second general objective is to investigate Host-type measure rigidity theory for toral automorphisms and homogeneous dynamics. This topic relates to currently ongoing research on measure classification theorems, which have been influential in several applications such Diophantine approximation and quantum ergodicity.

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Web resources:	https://cordis.europa.eu/project/id/655310
Start date:	01-09-2015
End date:	31-08-2017
Total budget - Public funding:	183 454,80 Euro - 183 454,00 Euro