Аннотация
The Guillemin-Uribe trace formula is a semiclassical version of the Selberg trace formula and the more general Duistermaat-Guillemin formula for elliptic operators on compact manifolds, which reflects the dynamics of magnetic geodesic flows in terms of eigenvalues of a natural differential operator (the magnetic Laplacian) associated with the magnetic field. This paper gives a survey of basic notions and results related to the Guillemin-Uribe trace formula and provides concrete examples of its computation for two-dimensional constant curvature surfaces with constant magnetic fields and for the Katok example. Bibliography: 53 titles.
Язык оригинала | английский |
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Номер статьи | 4 |
Страницы (с-по) | 325-361 |
Число страниц | 37 |
Журнал | Russian Mathematical Surveys |
Том | 74 |
Номер выпуска | 2 |
DOI | |
Состояние | Опубликовано - 1 янв 2019 |
ГРНТИ
- 29 ФИЗИКА