Page 1

Displaying 1 – 3 of 3

Showing per page

The action spectrum near positive definite invariant tori

Patrick Bernard (2003)

Bulletin de la Société Mathématique de France

We show that the Birkhoff normal form near a positive definite KAM torus is given by the function α of Mather. This observation is due to Siburg [Si2], [Si1] in dimension 2. It clarifies the link between the Birkhoff invariants and the action spectrum near the torus. Our extension to high dimension is made possible by a simplification of the proof given in [Si2].

The tiered Aubry set for autonomous Lagrangian functions

Marie-Claude Arnaud (2008)

Annales de l’institut Fourier

Let L : T M be a Tonelli Lagrangian function (with M compact and connected and dim M 2 ). The tiered Aubry set (resp. Mañé set) 𝒜 T ( L ) (resp. 𝒩 T ( L ) ) is the union of the Aubry sets (resp. Mañé sets) 𝒜 ( L + λ ) (resp. 𝒩 ( L + λ ) ) for λ closed 1-form. Then1.the set 𝒩 T ( L ) is closed, connected and if dim H 1 ( M ) 2 , its intersection with any energy level is connected and chain transitive;2.for L generic in the Mañé sense, the sets 𝒜 T ( L ) ¯ and 𝒩 T ( L ) ¯ have no interior;3.if the interior of 𝒜 T ( L ) ¯ is non empty, it contains a dense subset of periodic points.We then give an example...

Transport problems and disintegration maps

Luca Granieri, Francesco Maddalena (2013)

ESAIM: Control, Optimisation and Calculus of Variations

By disintegration of transport plans it is introduced the notion of transport class. This allows to consider the Monge problem as a particular case of the Kantorovich transport problem, once a transport class is fixed. The transport problem constrained to a fixed transport class is equivalent to an abstract Monge problem over a Wasserstein space of probability measures. Concerning solvability of this kind of constrained problems, it turns out that in some sense the Monge problem corresponds to a...

Currently displaying 1 – 3 of 3

Page 1