The partial captivity condition for U(1) extensions of expanding maps on the circle

被引：8

作者：

Nakano, Yushi ^{[1
]}

Tsujii, Masato ^{[2
]}

Wittsten, Jens ^{[3
]}

机构：

[1] Osaka City Univ, Adv Math Inst, Osaka 5588585, Japan

[2] Kyushu Univ, Dept Math, Fukuoka 8128581, Japan

[3] Ritsumeikan Univ, Dept Math Sci, Kusatsu 5258577, Japan

来源：

NONLINEARITY | 2016年 / 29卷 / 07期

关键词：

dynamical system; partially expanding map; partial captivity; transversality;

D O I：

10.1088/0951-7715/29/7/1917

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper concerns the compact group extension f: T-2 -> T-2, f(x, s)=(E(x), s + tau(x) mod 1) of an expanding map E : S-1 -> S-1. The dynamics of f and its stochastic perturbations have previously been studied under the so-called partial captivity condition. Here we prove a supplementary result that shows that partial captivity is a C-r generic condition on tau, once we fix E.

引用

页码：1917 / 1925

页数：9

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