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Regular Lagrangians are smooth Lagrangians

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arxiv 2407.00395 v2 pith:FEFHXWF4 submitted 2024-06-29 math.SG math.ATmath.CT

Tomohiro Asano , Stéphane Guillermou , Yuichi Ike , Claude Viterbo This is my paper · ORCID
classification math.SGmath.ATmath.CT
keywords smoothelementgammalagrangiancompactcompletionlagrangiansprove
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abstract

We prove that for any element in the $\gamma$-completion of the space of smooth compact exact Lagrangian submanifolds of a cotangent bundle, if its $\gamma$-support is a smooth Lagrangian submanifold, then the element itself is a smooth Lagrangian. We also prove that if the $\gamma$-support of an element in the completion is compact, then it is connected.

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  1. Birkhoff attractors for dissipative symplectic billiards

    math.DS 2025-09 conditional novelty 7.0 of 10

    A dissipative variant of symplectic billiards is introduced; its Birkhoff attractor is proved to be a normally contracted graph for strong dissipation, and an indecomposable continuum with positive topological entropy...

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