Equilibrium states for non-transitive random open and closed dynamical systems

Abstract We prove a random Ruelle–Perron–Frobenius theorem and the existence of relative equilibrium states for class open closed interval maps, without imposing transitivity requirements, such as mixing covering conditions, which are prevalent in literature. This provides uniqueness conformal invariant measures with exponential decay correlations, allows us to expand examples (random) dynamical systems amenable multiplicative ergodic theory thermodynamic formalism. Applications include non-transitive connection between Lyapunov exponents escape rates through holes. also able treat intermittent maps geometric potentials.