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Canonical models for holomorphic iteration


Authors: Leandro Arosio and Filippo Bracci
Journal: Trans. Amer. Math. Soc. 368 (2016), 3305-3339
MSC (2010): Primary 32H50; Secondary 39B12, 26A18
DOI: https://doi.org/10.1090/tran/6593
Published electronically: May 29, 2015
MathSciNet review: 3451878
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Abstract: We construct canonical intertwining semi-models with Kobayashi hyperbolic base space for holomorphic self-maps of complex manifolds which are univalent on some absorbing cocompact hyperbolic domain. In particular, in the unit ball we solve the Valiron equation for hyperbolic univalent self-maps and for hyperbolic semigroups.


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Additional Information

Leandro Arosio
Affiliation: Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via Della Ricerca Scientifica 1, 00133, Roma, Italy
Email: arosio@mat.uniroma2.it

Filippo Bracci
Affiliation: Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via Della Ricerca Scientifica 1, 00133, Roma, Italy
Email: fbracci@mat.uniroma2.it

DOI: https://doi.org/10.1090/tran/6593
Keywords: Iteration theory, linear fractional models, dynamics in several complex variables
Received by editor(s): March 4, 2014
Published electronically: May 29, 2015
Additional Notes: This work was supported by the ERC grant “HEVO - Holomorphic Evolution Equations” n. 277691
Article copyright: © Copyright 2015 American Mathematical Society

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