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

Yushi Nakano, Tsujii Masato, Jens Wittsten

Research output: Contribution to journalArticle

4 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 languageEnglish
Pages (from-to)1917-1925
Number of pages9
JournalNonlinearity
Volume29
Issue number7
DOIs
Publication statusPublished - May 25 2016

Fingerprint

Expanding Maps
Circle
Partial
Group Extension
Stochastic Perturbation
Compact Group
fixing
perturbation

All Science Journal Classification (ASJC) codes

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

Cite this

The partial captivity condition for U(1) extensions of expanding maps on the circle. / Nakano, Yushi; Masato, Tsujii; Wittsten, Jens.

In: Nonlinearity, Vol. 29, No. 7, 25.05.2016, p. 1917-1925.

Research output: Contribution to journalArticle

Nakano, Yushi ; Masato, Tsujii ; Wittsten, Jens. / The partial captivity condition for U(1) extensions of expanding maps on the circle. In: Nonlinearity. 2016 ; Vol. 29, No. 7. pp. 1917-1925.
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