Title :

Spectral analysis of Morse-Smale gradient flows

Author(s) :

Dang, Nguyen Viet [Auteur]
Institut Camille Jordan [ICJ]
Probabilités, statistique, physique mathématique [PSPM]
Riviere, Gabriel [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Annales Scientifiques de l'École Normale Supérieure

Publisher :

Société mathématique de France

Publication date :

2019

ISSN :

0012-9593

English keyword(s) :

Morse theory
gradient flow
resonances
transfer operator
differential topology

HAL domain(s) :

Mathématiques [math]/Systèmes dynamiques [math.DS]
Mathématiques [math]/Topologie géométrique [math.GT]
Mathématiques [math]/Théorie spectrale [math.SP]

English abstract : [en]

On a smooth, compact and oriented manifold without boundary, we give a complete description of the correlation function of a Morse-Smale gradient flow satisfying a certain nonresonance assumption. This is done by analyzing ...
Show more >On a smooth, compact and oriented manifold without boundary, we give a complete description of the correlation function of a Morse-Smale gradient flow satisfying a certain nonresonance assumption. This is done by analyzing precisely the spectrum of the generator of such a flow acting on certain anisotropic spaces of currents. In particular, we prove that this dynamical spectrum is given by linear combinations with integer coefficients of the Lyapunov exponents at the critical points of the Morse function. Via this spectral analysis and in analogy with Hodge-de Rham theory, we give an interpretation of the Morse complex as the image of the de Rham complex under the spectral projector on the kernel of the generator of the flow. This allows us to recover classical results from differential topology such as the Morse inequalities and Poincaré duality.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

ANR Project :

Phénomènes de diffusion et de propagation près des horizons d'espace-temps

Comment :

Shortened version (56 p.), to appear in Annales Sci. ENS

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL