Contributions of non-extremum critical points to the semi-classical trace formula

Abstract

We study the semi-classical trace formula at a critical energy level for a $h$-pseudo-differential operator on ${\mathbb{R}}^n$ whose principal symbol has a totally degenerate critical point for that energy. We compute the contribution to the trace formula of isolated non-extremum critical points under a condition of "real principal type". The new contribution to the trace formula is valid for all time in a compact subset of $\mathbb{R}$ but the result is modest since we have restrictions on the dimension.

24 pages

Cited by in corpus (2)

• 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