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math.CV2023★ 2 cited
Monotonicity of dynamical degrees for H{é}non-like and polynomial-like maps
Fabrizio Bianchi, Tien-Cuong Dinh, Karim Rakhimov
We prove that, for every invertible horizontal-like map (i.e., H{é}non-like map) in any dimension, the sequence of the dynamical degrees is increasing until that of maximal value,…
math.CV2022
Generalized Levi currents and singular loci for families of plurisubharmonic functions
Fabrizio Bianchi, Samuele Mongodi
We show how the formalism of Levi currents on complex manifolds, as introduced by Sibony, can be used to study the analytic structure of singular sets associated to families of plu…
math.CV2014★ 1 cited
A Poincaré-Bendixson theorem for meromorphic connections on Riemann surfaces
Marco Abate, Fabrizio Bianchi
We prove a Poincaré-Bendixson theorem describing the asymptotic behavior of geodesics for a meromorphic connection on a compact Riemann surface. We shall also briefly discuss the c…