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math.CV2025
Iterated function systems of holomorphic maps
Marco Abate, Ian Short
We unify and advance a host of works on iterated function systems of holomorphic self-maps of hyperbolic Riemann surfaces. Our foremost result is a generalisation to left iterated…
math.CV2025
Parabolic dynamics according to Maurice Heins
Marco Abate
This paper, based upon an unpublished manuscript by Maurice Heins, answers a question posed by Valiron about the dynamics of parabolic self-maps of the unit disk in the complex pla…
math.CV2024
Dynamics of Fuchsian meromorphic connections with real periods
Marco Abate, Karim Rakhimov
In this paper, we study the dynamics of geodesics of Fuchsian meromorphic connections with real periods, giving a precise characterization of the possible -limit sets of simple…