40 citations · 78 across the 30 of their papers we have counts for
34 papers
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This paper, based upon an unpublished manuscript by Maurice Heins, answers a question posed by Valiron about the dynamics of parabolic self-maps of the unit disk in the complex pla…
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…
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…
Random iteration on hyperbolic Riemann surfaces
Marco Abate, Argyrios Christodoulou
Let be a sequence of holomorphic self-maps of a hyperbolic Riemann surface . In this paper we shall study the asymptotic behavior of the sequences obtained by iterativ…
Multipoint Julia theorems
Marco Abate
Following ideas introduced by Beardon-Minda and by Baribeau-Rivard-Wegert in the context of the Schwarz-Pick lemma, we use the iterated hyperbolic difference quotients to prove a m…
Toeplitz Operators and Skew Carleson measures for weighted Bergman spaces on strongly pseudoconvex domains
Marco Abate, Samuele Mongodi, Jasmin Raissy
In this paper we study mapping properties of Toeplitz-like operators on weighted Bergman spaces of bounded strongly pseudconvex domains in . In particular we prove th…