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Arnold Tongues for Discrete Hill’s Equation
Automatic Control Departament, CINVESTAV-IPN, Mexico City, Mexico
Automatic Control Departament, CINVESTAV-IPN, Mexico City, Mexico
- 1 Automatic Control Departament, CINVESTAV-IPN, Mexico City, Mexico
- 2 Automatic Control Departament, CINVESTAV-IPN, Mexico City, Mexico
Applied Mathematics·Volume 08 (2017)·Pages 1859–1882·Published 4 December 2017·DOI10.4236/am.2017.812133
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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.
KeywordsArnold TonguesDiscrete Hill’s EquationMonodromy MatrixDiscretized Hamiltonian
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