Degenerations of complex dynamical systems II: analytic and algebraic stability

作者：DeMarco Laura; Faber Xander^*

来源：Mathematische Annalen, 2016, 365(3-4): 1669-1699.

DOI：10.1007/s00208-015-1331-8

We study pairs consisting of a non-Archimedean rational function f and a finite set of vertices in the Berkovich projective line, under a certain stability hypothesis. We prove that stability can always be attained by enlarging the vertex set . As a byproduct, we deduce that meromorphic maps preserving the fibers of a rationally-fibered complex surface are algebraically stable after a proper modification. The first article in this series examined the limit of the equilibrium measures for a degenerating 1-parameter family of rational functions on the Riemann sphere. Here we construct a convergent countable-state Markov chain that computes the limit measure. A classification of the periodic Fatou components for non-Archimedean rational functions, due to Rivera-Letelier, plays a key role in the proofs of our main theorems. The appendix contains a proof of this classification for all tame rational functions.

• 出版日期2016-8
• 单位西北大学