Arnold Tongues for Discrete Hill’s Equation

• 作者: José Guillermo Rodríguez Servín M. Joaquin Collado
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: ARNOLD Tongues DISCRETE Hill’s EQUATION MONODROMY MATRIX Discretized HAMILTONIAN
• 年，卷（期）: 2017,（12）
• 页码范围: 1859-1882
• 页数: 24页
• 分类号: O1

摘要

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.