Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Aubry-Mather and weak KAM theories for contact Hamiltonian systems. Part
  1: Strictly increasing case   This paper is concerned with the study of Aubry-Mather and weak KAM theories
for contact Hamiltonian systems with Hamiltonians $H(x,u,p)$ defined on
$T^*M\times\mathbb{R}$, satisfying Tonelli conditions with respect to $p$ and
$0<\frac{\partial H}{\partial u}\leqslant \lambda$ for some $\lambda>0$, where
$M$ is a connected, closed and smooth manifold. First, we show the uniqueness
of the backward weak KAM solutions of the corresponding Hamilton-Jacobi
equation. Using the unique backward weak KAM solution $u_-$, we prove the
existence of the maximal forward weak KAM solution $u_+$. Next, we analyse
Aubry set for the contact Hamiltonian system showing that it is the
intersection of two Legendrian pseudographs $G_{u_-}$ and $G_{u_+}$, and that
the projection $\pi:T^*M\times \mathbb{R}\to M$ induces a bi-Lipschitz
homeomorphism $\pi|_{\tilde{\mathcal{A}}}$ from Aubry set $\tilde{\mathcal{A}}$
onto the projected Aubry set $\mathcal{A}$. At last, we introduce the notion of
barrier functions and study their interesting properties along calibrated
curves. Our analysis is based on a recent method by [43,44].

31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn