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Gel’fand, I.M. and Lidskii, V.B. (1955) On the Structure of the Regions of Stability of Linear Canonical Systems of Differential Equations with Periodic Coefficients. English Transl., Amer. Math. Soc. Transl. 10 Series 2, 143-181.

has been cited by the following article:

• TITLE: Arnold Tongues for Discrete Hill’s Equation

  AUTHORS: José Guillermo Rodríguez Servín, M. Joaquin Collado

  KEYWORDS: Arnold Tongues, Discrete Hill’s Equation, Monodromy Matrix, Discretized Hamiltonian

  JOURNAL NAME: Applied Mathematics, Vol.8 No.12, December 29, 2017

  ABSTRACT: In this work we study two types of Discrete Hill’s equation. The first comes from the discretization process of a Continuous-time Hill’s equation, we called Discretized Hill’s equation. The Second is a naturally obtained in Discrete-Time and will be called Discrete-time Hill’s equation. The objective of discretization is preserving the continuous-time behavior and we show this property. On the contrary a completely different dynamic property was found for the Discrete-Time Hill’s equation. At the end of the paper is shown that both types share the nonoscillatory behavior of solutions in the 0-th Arnold Tongue.