Limits of rational maps, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:mi mathvariant="double-struck">R</mml:mi></mml:math>-trees and barycentric extension
نویسندگان
چکیده
In this paper, we show that one can naturally associate a limiting dynamical system F:T⟶T on an R-tree to any degenerating sequence of rational maps fn:Cˆ⟶Cˆ fixed degree. The construction F is in 2 steps: first, use barycentric extension get Efn:H3⟶H3; second, take appropriate limit rescalings hyperbolic space. An important ingredient prove here the Lipschitz constant depends only degree map. We dynamics records length spectra fn.
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2021
ISSN: ['1857-8365', '1857-8438']
DOI: https://doi.org/10.1016/j.aim.2021.108075