Perturbations singulières et formules de localisation. (French) Zbl 0542.58023

Combet, Edmond

C. R. Acad. Sci., Paris, Sér. I 297, 59-65 (1983).

The analogy between the topological invariants of compact differentiable manifolds and the localization phenomena observed in nature (bifurcation, singular perturbation theory) is pointed out. Further the asymptotic properties of functional integrals (of the type Feynman-Kac) and indices of differential operators are considered. The author gives a simpler method to obtain some of these results.

Reviewer: A.O.Barut

MSC:

37G99	Local and nonlocal bifurcation theory for dynamical systems
37J40	Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion

Keywords:

topological invariants of compact differentiable manifolds; localization phenomena; asymptotic properties of functional integrals; indices of differential operators