Differential and Integral Equations

On the ergodic approach for the study of chaotic linear infinite dimensional systems

S. EL Mourchid and K. Latrach

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In this work, we will be interested in the study of chaotic behavior exhibited by some linear infinite-dimensional systems. Our tool for this is the theory of chaotic linear semigroups of operators, and we will make use of the imaginary eigenvalues of the infinitesimal generator to construct an invariant Gaussian measure with respect to which the associated semigroup will be strong mixing. An application to the dynamic of a size-structured cell population is given.

Article information

Differential Integral Equations, Volume 26, Number 11/12 (2013), 1321-1333.

First available in Project Euclid: 4 September 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 37L40: Invariant measures 28D10: One-parameter continuous families of measure-preserving transformations 35Q92: PDEs in connection with biology and other natural sciences 92D25: Population dynamics (general)


EL Mourchid, S.; Latrach, K. On the ergodic approach for the study of chaotic linear infinite dimensional systems. Differential Integral Equations 26 (2013), no. 11/12, 1321--1333. https://projecteuclid.org/euclid.die/1378327428

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