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This is an extended version of my talk at the Fractal Geometry and Stochastic V conference in Tabarz. It is based on my joint paper (Bochi and Rams, The entropy of Lyapunov-optimizing measures of some metric cocycles, preprint) with Jairo Bochi (PUC Santiago). Compared with the paper, I’ll skip some details of some proofs, but I’ll try to explain the main idea of our approach.

Entropy of Lyapunov-Optimizing Measures of Some Matrix Cocycles