Almost periodic structures and the semiconjugacy problem

J. Aliste-Prieto, T. Jäger

Resultado de la investigación: Research - revisión exhaustivaArticle

  • 3 Citas

Resumen

The description of almost periodic or quasiperiodic structures has a long tradition in mathematical physics, in particular since the discovery of quasicrystals in the early 80's. Frequently, the modelling of such structures leads to different types of dynamical systems which include, depending on the concept of quasiperiodicity being considered, skew products over quasiperiodic or almost periodic base flows, mathematical quasicrystals or maps of the real line with almost periodic displacement. An important problem in this context is to know whether the considered system is semiconjugate to a rigid translation. We solve this question in a general setting that includes all the above-mentioned examples and also allows the treatment of scalar differential equations that are almost periodic both in space and time. To that end, we study a certain class of flows that preserve a one-dimensional foliation and show that a semiconjugacy to a minimal translation flow exists if and only if a boundedness condition, concerning the distance of orbits of the flow to those of the translation, holds.

IdiomaEnglish
Páginas4988-5001
Número de páginas14
PublicaciónJournal of Differential Equations
Volumen252
Número de edición9
DOI
EstadoPublished - 1 may 2012

Huella dactilar

Periodic Structures
Almost Periodic
Quasicrystals
Quasiperiodicity
Skew Product
Foliation
Real Line
Boundedness
Dynamical system
Orbit
Physics
Scalar
Differential equation
If and only if
Modeling
Context
Class
Concepts

ASJC Scopus subject areas

  • Analysis

Citar esto

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Almost periodic structures and the semiconjugacy problem. / Aliste-Prieto, J.; Jäger, T.

En: Journal of Differential Equations, Vol. 252, N.º 9, 01.05.2012, p. 4988-5001.

Resultado de la investigación: Research - revisión exhaustivaArticle

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