The K-property for subadditive equilibrium states. Issue 1 (2nd January 2021) - Call, Benjamin; Park, Kiho
ABSTRACT: By generalizing Ledrappier's criterion [ Mesures d'èquilibre d'entropie complètement positive, in Systèmes dynamiques II – Varsovie, number 50 in Astérisque, Société mathématique de France, 1977, pp. 251–272] for the K -property of equilibrium states, we extend the criterion to subadditive potentials. In particular, supposing that the unique equilibrium state for a subadditive potential with quasi-multiplicativity and bounded distortion is totally ergodic, we show that it has the K-property. We apply this result to subadditive potentials arising from certain classes of matrix cocycles; for the norm potentials of irreducible locally constant cocycles and the singular value potentials of typical cocycles, we show that their unique equilibrium states have the K-property. This partly generalizes the work of Morris [ Ergodic properties of matrix equilibrium states, Ergodic Theory Dyn. Syst. 38(6), 2018, pp. 2295-2320] on irreducible locally constant cocycles and their subadditive equilibrium states.