This article applies the continuous Newton method to the Riemann zeta function and discusses the emerging patterns emphasizing especially the structuring of the non-trivial zeros by the separatrices.

This article proves that the dynamical system (f,μφ) enjoys exponential decay of correlations of Hölder continuous observables as well as the Central Limit Theorem and the Law of Iterated Logarithm for the class of these variables that, in addition, satisfy a natural co-boundary condition. This article also shows that the topological pressure function t ↦ P(tφ) is real-analytic throughout the open set of all parameters t for which the potentials tφ have pressure gaps.