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Gel’fand, I.M. and Lidskii, V.B. (1958) On the Structure of the Regions of Stability of Linear Canonical Systems of Differential Equations with Periodic Coefficients. Uspekhi Matematicheskikh Nauk, 10, 3-40 (English Translation: AMS Translations, Series 2, 2, 143-181).

has been cited by the following article:

• TITLE: Vibrational Stabilization by Reshaping Arnold Tongues: A Numerical Approach

  AUTHORS: Joaquin Collado, Hildeberto Jardón-Kojakhmetov

  KEYWORDS: Vibrational Stabilization, Hill Equation, Periodic Systems, Arnold Tongues

  JOURNAL NAME: Applied Mathematics, Vol.7 No.16, October 28, 2016

  ABSTRACT: This paper presents two contributions to the stability analysis of periodic systems modeled by a Hill equation: The first is a new method for the computation of the Arnold Tongues associated to a given Hill equation which is based on the discretization of the latter. Using the proposed method, a vibrational stabilization is performed by a change in the periodic function which guarantees stability, given that the original equation has unbounded solutions. The results are illustrated by some examples.