Forty years of unimodal dynamics: On theoccasion of Artur Avila winning the Brin Prize
Forty years of unimodal dynamics: On theoccasion of Artur Avila winning the Brin Prize
复制标题
四十年的单峰动力学：阿图尔·阿维拉 (Artur Avila) 荣获布林奖之际
DOI：
10.3934/jmd.2012.6.183
复制
发表时间：
2012
影响因子：
1.1
通讯作者：
M. Lyubich
中科院分区：
文献类型：
--
作者：
M. Lyubich
一维动力学领域，真实和复杂的，从默默无闻中出现在
20世纪70年代，从那时起，人们一直在激烈地探索。它
将混沌现象的深度和复杂性与
用概率术语完全理解它的机会：描述
典型地图的典型轨道动力学。它还揭示了
令人着迷的普遍性特征
以前从未被注意过。真实与复杂之间的相互作用
由美丽的分形结构图片照亮的世界增加了
给赛场带来特别的魅力。
到目前为止，我们已经对REAL达成了完全的概率理解
解析单峰动力学，阿图尔·阿维拉一直是
故事的最后阶段(大致从新的
世纪)。为了正确看待他的工作，我们将从一个
从20世纪70年代到结束这一领域的主要事件概述
上个世纪。然后我们将描述Avila在单峰方面的工作
有效地关闭了场地的动态。我们将在以下时间结束
描述他在密切相关的方向上的结果，几何学
，包括最近构造的一个新的
正面积的Julia集的类。
The field of one-dimensional dynamics, real and complex, emerged from obscurity in
the 1970s and has been intensely explored ever since. It
combines the depth and complexity of chaotic phenomena with a
chance to fully understand it in probabilistic terms: to describe the
dynamics of typical orbits for typical maps. It also revealed
fascinating universality features that
had never been noticed before. The interplay between real and complex
worlds illuminated by beautiful pictures of fractal structures adds
special charm to the field.
By now, we have reached a full probabilistic understanding of real
analytic unimodal dynamics, and Artur Avila has been the key player in
the final stage of the story (which roughly started with the new
century). To put his work into perspective, we will begin with an
overview of the main events in the field from the 1970s up to the end
of the last century. Then we will describe Avila's work on unimodal
dynamics that effectively closed up the field. We will finish by
describing his results in the closely related direction, the geometry
of Feigenbaum Julia sets, including a recent construction of a new
class of Julia sets of positive area.