Spectral analysis and an area-preserving extension of a piecewise linear intermittent map

Tomoshige Miyaguchi*, Yoji Aizawa

*この研究の対応する著者

研究成果: Article査読

13 被引用数 (Scopus)

抄録

We investigate the spectral properties of a one-dimensional piecewise linear intermittent map, which has not only a marginal fixed point but also a singular structure suppressing injections of the orbits into neighborhoods of the marginal fixed point. We explicitly derive generalized eigenvalues and eigenfunctions of the Frobenius-Perron operator of the map for classes of observables and piecewise constant initial densities, and it is found that the Frobenius-Perron operator has two simple real eigenvalues 1 and λd (-1,0) and a continuous spectrum on the real line [0,1]. From these spectral properties, we also found that this system exhibits a power law decay of correlations. This analytical result is found to be in a good agreement with numerical simulations. Moreover, the system can be extended to an area-preserving invertible map defined on the unit square. This extended system is similar to the baker transformation, but does not satisfy hyperbolicity. A relation between this area-preserving map and a billiard system is also discussed.

本文言語English
論文番号066201
ジャーナルPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
75
6
DOI
出版ステータスPublished - 2007 6月 4

ASJC Scopus subject areas

  • 物理学および天文学(全般)
  • 凝縮系物理学
  • 統計物理学および非線形物理学
  • 数理物理学

フィンガープリント

「Spectral analysis and an area-preserving extension of a piecewise linear intermittent map」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル