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

Yushi Nakano; Masato Tsujii; Jens Wittsten

doi:10.1088/0951-7715/29/7/1917

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

Yushi Nakano, Masato Tsujii, Jens Wittsten

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

This paper concerns the compact group extension f : ⌉2→⌉2, f (x, s) = (E(x), s + τ(x) mod 1) of an expanding map E : S¹→S¹. 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 τ generic condition on τ, once we fix E.

Original language	English
Pages (from-to)	1917-1925
Number of pages	9
Journal	Nonlinearity
Volume	29
Issue number	7
DOIs	https://doi.org/10.1088/0951-7715/29/7/1917
Publication status	Published - May 25 2016

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics
Physics and Astronomy(all)
Applied Mathematics

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AB - This paper concerns the compact group extension f : ⌉2→⌉2, f (x, s) = (E(x), s + τ(x) mod 1) of an expanding map E : S1→S1. 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 τ generic condition on τ, once we fix E.

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