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From KAM Theory to Aubry-Mather Theory

From KAM Theory to Aubry-Mather Theory

Chapter:
(p.8) Chapter Two From KAM Theory to Aubry-Mather Theory
Source:
Action-minimizing Methods in Hamiltonian Dynamics (MN-50)
Author(s):
Alfonso Sorrentino
Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691164502.003.0002

This chapter discusses an illustrative example, namely the properties of invariant probability measures and orbits on KAM tori (or more generally, on invariant Lagrangian graphs). This will prepare the ground for understanding the main ideas and techniques that will be developed in the following chapters, without several technicalities that might be confusing to a neophyte.

Keywords:   KAM tori, invariant Lagrangian graphs, orbits, invariant probability measures

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