Introduction to KAM theory
Summary
This thesis aims to provide an introduction to modern KAM theory.
This objective is accomplished by introducing the fundamental ideas of KAM
theory, including its background, commonly used methods, and the general
structure of a KAM proof. Additionally, the thesis discusses parameter
reduction and the generalizations of the Diophantine conditions. The
culmination of the thesis is a complete proof of the classical KAM theorem,
but the primary focus remains pedagogical and expository throughout.
It is important to note that while the thesis covers a broad range of topics, it
does not aim to provide a systematic survey of all the methods found in KAM
theory. Instead, the emphasis is on presenting the traditional KAM method
and its key ideas in a clear and accessible manner.