We show that if f : B-q -> B-q is a holomorphic self-map of the unit ball in C-q and zeta is an element of partial derivative B-q is a boundary repelling fixed point with dilation lambda > 1, then there exists a backward orbit converging to zeta with step log lambda. Morever, any two backward orbits converging to the same boundary repelling fixed point stay at finite distance. As a consequence there exists a unique canonical premodel (B-k, l, t) associated with zeta where 1 <= k <= q, t is a hyperbolic automorphism of B-k, and whose image l(B-k) is precisely the set of starting points of backward orbits with bounded step converging to zeta. This answers questions of Ostapyuk (2011) and the first author (2015, 2017).

Arosio, L., Guerini, L. (2019). Backward orbits in the unit ball. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 147(9), 3947-3954 [10.1090/proc/14544].

Backward orbits in the unit ball

Arosio L.;
2019-01-01

Abstract

We show that if f : B-q -> B-q is a holomorphic self-map of the unit ball in C-q and zeta is an element of partial derivative B-q is a boundary repelling fixed point with dilation lambda > 1, then there exists a backward orbit converging to zeta with step log lambda. Morever, any two backward orbits converging to the same boundary repelling fixed point stay at finite distance. As a consequence there exists a unique canonical premodel (B-k, l, t) associated with zeta where 1 <= k <= q, t is a hyperbolic automorphism of B-k, and whose image l(B-k) is precisely the set of starting points of backward orbits with bounded step converging to zeta. This answers questions of Ostapyuk (2011) and the first author (2015, 2017).
2019
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/03 - GEOMETRIA
English
Backward orbits; canonical models; holomorphic iteration
Arosio, L., Guerini, L. (2019). Backward orbits in the unit ball. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 147(9), 3947-3954 [10.1090/proc/14544].
Arosio, L; Guerini, L
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/242245
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