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Media type:
E-Article
Title:
Recurrent-Proximal Linear Differential Systems with Almost Periodic Coefficients
Contributor:
Nerurkar, Mahesh G.
Published:
American Mathematical Society, 1987
Published in:
Proceedings of the American Mathematical Society, 100 (1987) 4, Seite 739-743
Language:
English
ISSN:
1088-6826;
0002-9939
Origination:
Footnote:
Description:
<p>We consider a system of linear differential equations,<tex-math>$\dot x = A(\omega \cdot t)x$</tex-math>, parametrized by a point ω ∈ T<sup>2</sup>, the 2-torus, where (ω, t) → ω · t denotes an irrational rotation flow on T<sup>2</sup>. We show that if the rotation number of this flow is well approximable by rationals, then residually many equations (with respect to the C<sup>k</sup>-topology on a certain class of matrix valued maps A(ω) on T<sup>2</sup>) exhibit recurrent-proximal behavior. Also the order of differentiability k of the class in which this generic result holds is related to the "speed" of approximation by rationals.</p>