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.