This is a tutorial on some of the main ideas in KAM theory. The goal is to present the
background and to explain and compare somewhat informally some of the main methods of …

Starting with the basics of Hamiltonian dynamics and canonical transformations, this text
follows the historical development of the theory culminating in recent results: the …

Kolmogorov-Arnold-Moser (or kam) theory was developed for conservative dynamical
systems that are nearly integrable. Integrable systems in their phase space usually contain …

Kolmogorov–Arnold–Moser (or KAM) Theory was developed for conservative (Hamiltonian)
dynamical systems that are nearly integrable. Integrable systems in their phase space …

ABSTRACT Kolmogorov-Arnol'd-Moser Theory classically was mainly developed for
conservative systems, establishing persistence results for quasi-periodic invariant tori in …

Discrete Holomorphic Local Dynamical Systems Page 1 Discrete Holomorphic Local
Dynamical Systems Marco Abate Abstract This chapter is a survey on local dynamics of …

This is a survey about local holomorphic dynamics, from Poincaré's times to nowadays.
Some new ideas on how to relate discrete dynamics to continuous dynamics are also …

Let f be a germ of holomorphic diffeomorphism of C^ n fixing the origin O, with df O
diagonalizable. We prove that, under certain arithmetic conditions on the eigenvalues of df O …

We explain Ecalle's''arbomould formalism''in its simplest instance, showing how it allows one
to give explicit formulas for the operators naturally attached to a germ of holomorphic map in …

2 FILIPPO BRACCI and it is still today a very flourishing sector of mathematics. Much of this
theory has been used and improved by people interested in the dynamics of holomorphic …