A semi-classical trace formula at a non-degenerate critical level

Abstract

We study the semi-classical trace formula at a critical energy level for a $h$-pseudo-differential operator whose principal symbol has a unique non-degenerate critical point for that energy. This leads to the study of Hamiltonian systems near equilibrium and near the non-zero periods of the linearized flow. The contributions of these periods to the trace formula are expressed in terms of degenerate oscillatory integrals. The new results obtained are formulated in terms of the geometry of the energy surface and the classical dynamics on this surface.

Repost of a paper published in 2004. 35 pages

Cited by in corpus (7)

• A semi-classical trace formula at a totally degenerate critical level
• Inverse Spectral Problem for Schrödinger Operators
• Contributions of non-extremum critical points to the semi-classical trace formula
• Semi-classical spectral estimates for Schrödinger operators at a critical level. Case of a degenerate maximum of the potential
• Semiclassical spectral estimates for Schrödinger operators at a critical energy level. Case of a degenerate potential
• Spectral estimates for degenerate critical levels
• Asymptotic approximation of degenerate fiber integrals