- 97-325 A. Candel, R. de la Llave
- On the Aubry--Mather theory in statistical mechanics
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Jun 11, 97
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Abstract. We generalize Aubry-Mather theory for configurations on the
line to general sets with a group action. Cocycles on the group play
the role of rotation numbers. The notion of Birkhoff configuration
can be generalized to this setting.
Under mild conditions on the group, we show how to find Birkhoff ground states
for many-body interactions which are ferromagnetic, invariant under the
group action and having periodic phase space.