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Sur la formule semi-classique des traces. (On the semi-classical trace formula). (French. Abridged English version) Zbl 0738.58046
For a class of $$h$$-pseudo-differential operators $$a(x,hD_ x)$$ on the manifold $$M$$ the asymptotics of $L(m,\varphi)=(1/m)\sum_{1\leq k\leq m}\hbox{Tr }\varphi[(a(x,hD_ x)-E)/h]\mid_{h=1/k}$ is obtained for $$m\to+\infty$$ where $$\varphi$$ is the function with the Fourier transform $$\hat\varphi\in C^ \infty_ 0$$ vanishing of the order $$\dim M$$ at 0. The limit of $$L(m,\varphi)$$ is calculated in terms of the periodic Hamiltonian trajectories of the principal symbol.

##### MSC:
 58J40 Pseudodifferential and Fourier integral operators on manifolds 37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems