Title | Reducibility for a fast-driven linear Klein–Gordon equation |

Publication Type | Journal Article |

Year of Publication | 2019 |

Authors | Franzoi, L, Maspero, A |

Volume | 198 |

Issue | 4 |

Pagination | 1407 - 1439 |

Date Published | 2019/08/01 |

ISBN Number | 1618-1891 |

Abstract | We prove a reducibility result for a linear Klein–Gordon equation with a quasi-periodic driving on a compact interval with Dirichlet boundary conditions. No assumptions are made on the size of the driving; however, we require it to be fast oscillating. In particular, provided that the external frequency is sufficiently large and chosen from a Cantor set of large measure, the original equation is conjugated to a time-independent, diagonal one. We achieve this result in two steps. First, we perform a preliminary transformation, adapted to fast oscillating systems, which moves the original equation in a perturbative setting. Then, we show that this new equation can be put to constant coefficients by applying a KAM reducibility scheme, whose convergence requires a new type of Melnikov conditions. |

URL | https://doi.org/10.1007/s10231-019-00823-2 |

Short Title | Annali di Matematica Pura ed Applicata (1923 -) |

## Reducibility for a fast-driven linear Klein–Gordon equation

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