Arnold Tongues for Discrete Hill’s Equation  

作　　者：José Guillermo Rodríguez Servín M. Joaquin Collado 

机构地区：[1]Automatic Control Departament, CINVESTAV-IPN, Mexico City, Mexico

出　　处：《Applied Mathematics》2017年第12期1859-1882,共24页应用数学（英文）

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.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.

关 键 词：ARNOLD Tongues DISCRETE Hill’s EQUATION MONODROMY MATRIX Discretized HAMILTONIAN 

分 类 号：O1[理学—数学]