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Ahlbrandt, C.D. and Peterson, A.C. (1996) Discrete Hamiltonian Systems: Difference Equations, Continued Fractions, and Riccati Equations. Springer US, Berlin. https://doi.org/10.1007/978-1-4757-2467-7

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.