@inproceedings{9949d563c7b344cda9f7ea78f9fa8447,
title = "Analytic low-dimensional dynamics: From dimension one to two",
abstract = "Let f: M → M be an analytic (real or complex) self-map of a manifold, and let fn stand for its n-fold iterate. The theory of Analytic Dynamical Systems with discrete time is concerned with understanding the asymptotic behavior of orbits (fnx). The main goal, as it was articulated in the second half of 20th century, is to describe, in probabilistic terms, the asymptotic distribution of typical orbits for typical systems. This goal is now achieved for unimodal one-dimensional maps, a great progress has been made in complex one-dimensional case, and a transition to the dissipative twodimensional situation, real and complex, is underway. Renormalization ideas played a crucial role in this story. We will describe all these developments in their interplay.",
keywords = "A priori bounds, Attractor, Henon map, Homoclinic tangency, Hyperbolicity, Julia set, Renormalization, Structural stability",
author = "Mikhail Lyubich",
note = "Publisher Copyright: {\textcopyright} 2014 by SEOULICM 2014 Organizing Committee. All rights reserved.; 2014 International Congress of Mathematicans, ICM 2014 ; Conference date: 13-08-2014 Through 21-08-2014",
year = "2014",
language = "English",
series = "Proceeding of the International Congress of Mathematicans, ICM 2014",
publisher = "KYUNG MOON SA Co. Ltd.",
pages = "443--474",
editor = "Jang, \{Sun Young\} and Kim, \{Young Rock\} and Dae-Woong Lee and Ikkwon Yie",
booktitle = "Plenary Lectures and Ceremonies",
}