Recurrent-proximal linear differential systems with almost periodic coefficients
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- by Mahesh G. Nerurkar PDF
- Proc. Amer. Math. Soc. 100 (1987), 739-743 Request permission
Abstract:
We consider a system of linear differential equations, $\dot x = A(\omega \cdot t)x$, parametrized by a point $\omega \in {{\mathbf {T}}^2}$, the $2$-torus, where $(\omega ,t) \to \omega \cdot t$ denotes an irrational rotation flow on ${{\mathbf {T}}^2}$. We show that if the rotation number of this flow is well approximable by rationals, then residually many equations (with respect to the ${C^k}$-topology on a certain class of matrix valued maps $A(\omega )$ on ${{\mathbf {T}}^2}$) 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.References
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Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 100 (1987), 739-743
- MSC: Primary 58F27; Secondary 34C28, 54H20
- DOI: https://doi.org/10.1090/S0002-9939-1987-0894447-0
- MathSciNet review: 894447