| Continuous time Hill’s equation | Discrete time Hill’s equation |

Is a Hamiltonian system? | yes | yes |

Its Monodromy matrix is symplectic? | yes | yes |

Numbers of Arnold tongues | generically $\infty $ | $K+1$ |

Arnold Tongues begin at | $\alpha ={\left(\frac{k\text{\pi}}{T}\right)}^{2}$ $k=0,1,2,\cdots $ | $\left|{\displaystyle \sum _{j=0}^{\frac{K-i}{2}}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}{l}_{j}{\left(-\alpha \right)}^{K-2j}\right|=2$ ${l}_{j}$ and $i$ as in theorem 12 |

Periodic/anti-periodicsolution alternation in the boundaries of the Arnold Tongues? | yes | yes |

0-th Arnold tongue has a nonoscillatory solution? | yes | yes |