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On the dynamics of Riccati foliations with nonparabolic monodromy representations
2019
Conformal Geometry and Dynamics
In this paper, we study the dynamics of Riccati foliations over noncompact finite volume Riemann surfaces. More precisely, we are interested in two closely related questions: the asymptotic behaviour of the holonomy map Hol t (ω) defined for every time t over a generic Brownian path ω in the base; and the analytic continuation of holonomy germs of the foliation along Brownian paths in transversal complex curves. When the monodromy representation is parabolic (i.e., the monodromy around any
doi:10.1090/ecgd/337
fatcat:sgqng7fxfnerrlc7f7wjyg3eaa