[PDF][PDF] Differentiability of Mather's average action and integrability on closed surfaces
D Massart, A Sorrentino - arXiv preprint arXiv:0907.2055, 2009 - arxiv.org
arXiv preprint arXiv:0907.2055, 2009•arxiv.org
… In Section 2 we provide a brief overview of Mather’s theory for Tonelli Lagrangian systems
and introduce the minimal average action, or β function. In Section 3 we discuss several
properties of the β function associated to Lagrangians on closed surfaces, with particular
attention to the implications of its differentiability, or the lack thereof, to the structure of the
Mather and Aubry sets. We consider both orientable and non-orientable surfaces, pointing out
the differences between the two cases. Finally in Section 4 we introduce the concept of C0-…
and introduce the minimal average action, or β function. In Section 3 we discuss several
properties of the β function associated to Lagrangians on closed surfaces, with particular
attention to the implications of its differentiability, or the lack thereof, to the structure of the
Mather and Aubry sets. We consider both orientable and non-orientable surfaces, pointing out
the differences between the two cases. Finally in Section 4 we introduce the concept of C0-…
In this article we study the differentiability of Mather's -function on closed surfaces and its relation to the integrability of the system.
arxiv.org
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