• 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>
  • Access State: Open Access