DEFORMATION THEORY OF ONE-DIMENSIONAL SYSTEMS

被引：0

作者：

Smania, Daniel ^{[1
]}

机构：

[1] Univ Sao Paulo, Dept Matemat, Inst Ciencias Matemat & Computacao, ICMC, Ave Trabalhador Sao Carlense,400 Ctr, BR-13566590 Sao Carlos, SP, Brazil

来源：

JOURNAL OF MODERN DYNAMICS | 2022年 / 21卷

基金：

巴西圣保罗研究基金会;

关键词：

Topological classes; ergodic theory; Birkhoff sums; deformation; LINEAR-RESPONSE; SMOOTH DEFORMATIONS; CIRCLE; DYNAMICS; ANOSOV; MAPS; RENORMALIZATION; HOMEOMORPHISMS; UNIVERSALITY; CONJUGACY;

D O I：

10.3934/jmd.2025001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

. We discuss a remarkable phenomenon which occurs in one-dimensional dynamics, that is, for maps acting on an interval or a circle. Such maps are often not structurally stable, however their topological class is an infinite dimensional smooth manifold with finite codimension. Consequently, the deformation theory of such systems is quite rich. Recent developments suggest that the study of the existence, uniqueness and regularity of solutions for certain cohomological equations is crucial for deeper understanding of these phenomena, and ergodic theory plays an important role in this study.

引用

页码：1 / 20

页数：20

共 61 条

[1] GEODESIC-FLOWS, INTERVAL MAPS, AND SYMBOLIC DYNAMICS [J].