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

Yushi Nakano, Masato Tsujii, Jens Wittsten

Research output: Contribution to journal › Article

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; Tsujii, Masato; Wittsten, Jens.

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

Research output: Contribution to journal › Article

Nakano, Y, Tsujii, M & Wittsten, J 2016, 'The partial captivity condition for U(1) extensions of expanding maps on the circle', Nonlinearity, vol. 29, no. 7, pp. 1917-1925. https://doi.org/10.1088/0951-7715/29/7/1917
Nakano Y, Tsujii M, Wittsten J. The partial captivity condition for U(1) extensions of expanding maps on the circle. Nonlinearity. 2016 May 25;29(7):1917-1925. https://doi.org/10.1088/0951-7715/29/7/1917
Nakano, Yushi ; Tsujii, Masato ; 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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