Centre de diffusion de revues académiques mathématiques

 
 
 
 

Journées équations aux dérivées partielles

Table des matières de ce volume | Article précédent | Article suivant
Nguyen Viet Dang; Gabriel Rivière
Correlation spectrum of Morse-Smale gradient flows
Journées équations aux dérivées partielles (2017), Exp. No. 6, 13 p., doi: 10.5802/jedp.656
Article PDF

Résumé - Abstract

In this note, we review our recent works devoted to the spectral analysis of Morse-Smale flows. Then we give applications to differential topology and to the spectral theory of Witten Laplacians.

Bibliographie

[1] V. Baladi & M. Tsujii, Dynamical determinants and spectrum for hyperbolic diffeomorphisms, Geometric and probabilistic structures in dynamics, Contemp. Math. 469, Amer. Math. Soc., Providence, RI, 2008, p. 29–68
[2] J.-M. Bismut & W. Zhang, “An extension of a theorem by Cheeger and Müller”, Astérisque (1992) no. 205, With an appendix by François Laudenbach
[3] M. Blank, G. Keller & C. Liverani, “Ruelle-Perron-Frobenius spectrum for Anosov maps”, Nonlinearity 15 (2002) no. 6, p. 1905-1973
[4] R. Brunetti & K. Fredenhagen, “Microlocal Analysis and Interacting Quantum Field Theories: Renormalization on Physical Backgrounds”, Comm. Math. Phys. 208 (2000) no. 3, p. 623-661
[5] O. Butterley & C. Liverani, “Smooth Anosov flows: correlation spectra and stability”, J. Mod. Dyn. 1 (2007) no. 2, p. 301-322
[6] N.V. Dang, “Renormalization of quantum field theory on curved space-times, a causal approach”, arXiv preprint arXiv:1312.5674 (2013)
[7] N.V. Dang, “The extension of distributions on manifolds, a microlocal approach”, Ann. Henri Poincaré 17 (2016) no. 4, p. 819-859
[8] N.V. Dang & G. Rivière, “Spectral analysis of Morse-Smale gradient flows”, (2016), Preprint arXiv:1605.05516
[9] N.V. Dang & G. Rivière, “Pollicott-Ruelle spectrum and Witten Laplacians”, arXiv preprint arXiv:1709.04265 (2017)
[10] N.V. Dang & G. Rivière, “Spectral analysis of Morse-Smale flows I: Construction of the anisotropic Sobolev spaces”, (2017), Preprint arXiv:1703.08040
[11] N.V. Dang & G. Rivière, “Spectral analysis of Morse-Smale flows II: Resonances and resonant states”, (2017), Preprint arXiv:1703.08038
[12] N.V. Dang & G. Rivière, “Topology of Pollicott-Ruelle resonant states”, (2017), Preprint arXiv:1703.08037
[13] S. Dyatlov & M. Zworski, “Stochastic stability of Pollicott-Ruelle resonances”, Nonlinearity 28 (2015) no. 10, p. 3511-3533
[14] S. Dyatlov & M. Zworski, “Dynamical zeta functions for Anosov flows via microlocal analysis”, Ann. Sci. Éc. Norm. Supér. (4) 49 (2016) no. 3, p. 543-577
[15] S. Dyatlov & M. Zworski, “Ruelle zeta function at zero for surfaces”, Inv. Math. (2017), To appear
[16] F. Faure & J. Sjöstrand, “Upper bound on the density of Ruelle resonances for Anosov flows”, Comm. Math. Phys. 308 (2011) no. 2, p. 325-364
[17] E. Frenkel, A. Losev & N. Nekrasov, “Instantons beyond topological theory. I”, J. Inst. Math. Jussieu 10 (2011) no. 3, p. 463-565
[18] D. Fried, Lefschetz formulas for flows, The Lefschetz centennial conference, Part III (Mexico City, 1984), Contemp. Math. 58, Amer. Math. Soc., Providence, RI, 1987, p. 19–69
[19] F.R. Harvey & H.B. Lawson, Morse theory and Stokes’ theorem, Surveys in differential geometry, Surv. Differ. Geom., VII, Int. Press, Somerville, MA, 2000, p. 259–311
[20] F.R. Harvey & H.B. Lawson, “Finite volume flows and Morse theory”, Ann. of Math. (2) 153 (2001) no. 1, p. 1-25
[21] B. Helffer & J. Sjöstrand, “Puits multiples en mécanique semi-classique. IV. Étude du complexe de Witten”, Comm. Partial Differential Equations 10 (1985) no. 3, p. 245-340
[22] F. Laudenbach, Transversalité, courants et théorie de Morse, Éditions de l’École Polytechnique, Palaiseau, 2012, Un cours de topologie différentielle. [A course of differential topology],
[23] C. Liverani, “On contact Anosov flows”, Ann. of Math. (2) 159 (2004) no. 3, p. 1275-1312
[24] G. Minervini, “A current approach to Morse and Novikov theories”, Rend. Mat. Appl. (7) 36 (2015) no. 3-4, p. 95-195
[25] E. Nelson, Topics in dynamics. I: Flows, Mathematical Notes, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1969
[26] J. Palis & W. de Melo, Geometric theory of dynamical systems, Springer-Verlag, New York-Berlin, 1982, An introduction, Translated from the Portuguese by A. K. Manning
[27] L. Schwartz, Théorie des distributions, Publications de l’Institut de Mathématique de l’Université de Strasbourg, No. IX-X., Hermann, Paris, 1966
[28] S. Smale, “Morse inequalities for a dynamical system”, Bull. Amer. Math. Soc. 66 (1960), p. 43-49
[29] R. Thom, “Sur une partition en cellules associée à une fonction sur une variété”, C. R. Acad. Sci. Paris 228 (1949), p. 973-975
[30] M. Tsujii, “Quasi-compactness of transfer operators for contact Anosov flows”, Nonlinearity 23 (2010) no. 7, p. 1495-1545
[31] M. Tsujii, “Contact Anosov flows and the Fourier-Bros-Iagolnitzer transform”, Ergodic Theory Dynam. Systems 32 (2012) no. 6, p. 2083-2118
[32] J. Weber, “The Morse-Witten complex via dynamical systems”, Expo. Math. 24 (2006) no. 2, p. 127-159
[33] E. Witten, “Supersymmetry and Morse theory”, J. Differential Geom. 17 (1982) no. 4, p. 661-692 (1983)
Copyright Cellule MathDoc 2018 | Crédit | Plan du site