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.
@incollection{JEDP_2017____A6_0,
author = {Nguyen Viet Dang and Gabriel Rivi\`ere},
title = {Correlation spectrum of {Morse-Smale} gradient flows},
booktitle = {},
series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
note = {talk:6},
pages = {1--13},
publisher = {Groupement de recherche 2434 du CNRS},
year = {2017},
doi = {10.5802/jedp.656},
language = {en},
url = {https://proceedings.centre-mersenne.org/articles/10.5802/jedp.656/}
}
TY - JOUR AU - Nguyen Viet Dang AU - Gabriel Rivière TI - Correlation spectrum of Morse-Smale gradient flows JO - Journées équations aux dérivées partielles N1 - talk:6 PY - 2017 SP - 1 EP - 13 PB - Groupement de recherche 2434 du CNRS UR - https://proceedings.centre-mersenne.org/articles/10.5802/jedp.656/ DO - 10.5802/jedp.656 LA - en ID - JEDP_2017____A6_0 ER -
%0 Journal Article %A Nguyen Viet Dang %A Gabriel Rivière %T Correlation spectrum of Morse-Smale gradient flows %J Journées équations aux dérivées partielles %Z talk:6 %D 2017 %P 1-13 %I Groupement de recherche 2434 du CNRS %U https://proceedings.centre-mersenne.org/articles/10.5802/jedp.656/ %R 10.5802/jedp.656 %G en %F JEDP_2017____A6_0
Nguyen Viet Dang; Gabriel Rivière. Correlation spectrum of Morse-Smale gradient flows. Journées équations aux dérivées partielles (2017), Exposé no. 6, 13 p. doi : 10.5802/jedp.656. https://proceedings.centre-mersenne.org/articles/10.5802/jedp.656/
[1] Dynamical determinants and spectrum for hyperbolic diffeomorphisms, Geometric and probabilistic structures in dynamics (Contemp. Math.), Volume 469, Amer. Math. Soc., Providence, RI, 2008, pp. 29-68
[2] An extension of a theorem by Cheeger and Müller, Astérisque (1992) no. 205, 235 pages (With an appendix by François Laudenbach)
[3] Ruelle-Perron-Frobenius spectrum for Anosov maps, Nonlinearity, Volume 15 (2002) no. 6, pp. 1905-1973
[4] Microlocal Analysis and Interacting Quantum Field Theories: Renormalization on Physical Backgrounds, Comm. Math. Phys., Volume 208 (2000) no. 3, pp. 623-661
[5] Smooth Anosov flows: correlation spectra and stability, J. Mod. Dyn., Volume 1 (2007) no. 2, pp. 301-322
[6] Renormalization of quantum field theory on curved space-times, a causal approach, arXiv preprint arXiv:1312.5674 (2013)
[7] The extension of distributions on manifolds, a microlocal approach, Ann. Henri Poincaré, Volume 17 (2016) no. 4, pp. 819-859
[8] Spectral analysis of Morse-Smale gradient flows (2016) (Preprint arXiv:1605.05516)
[9] Pollicott-Ruelle spectrum and Witten Laplacians, arXiv preprint arXiv:1709.04265 (2017)
[10] Spectral analysis of Morse-Smale flows I: Construction of the anisotropic Sobolev spaces (2017) (Preprint arXiv:1703.08040)
[11] Spectral analysis of Morse-Smale flows II: Resonances and resonant states (2017) (Preprint arXiv:1703.08038)
[12] Topology of Pollicott-Ruelle resonant states (2017) (Preprint arXiv:1703.08037)
[13] Stochastic stability of Pollicott-Ruelle resonances, Nonlinearity, Volume 28 (2015) no. 10, pp. 3511-3533
[14] Dynamical zeta functions for Anosov flows via microlocal analysis, Ann. Sci. Éc. Norm. Supér. (4), Volume 49 (2016) no. 3, pp. 543-577
[15] Ruelle zeta function at zero for surfaces, Inv. Math. (2017) (To appear)
[16] Upper bound on the density of Ruelle resonances for Anosov flows, Comm. Math. Phys., Volume 308 (2011) no. 2, pp. 325-364
[17] Instantons beyond topological theory. I, J. Inst. Math. Jussieu, Volume 10 (2011) no. 3, pp. 463-565
[18] Lefschetz formulas for flows, The Lefschetz centennial conference, Part III (Mexico City, 1984) (Contemp. Math.), Volume 58, Amer. Math. Soc., Providence, RI, 1987, pp. 19-69
[19] Morse theory and Stokes’ theorem, Surveys in differential geometry (Surv. Differ. Geom., VII), Int. Press, Somerville, MA, 2000, pp. 259-311
[20] Finite volume flows and Morse theory, Ann. of Math. (2), Volume 153 (2001) no. 1, pp. 1-25
[21] Puits multiples en mécanique semi-classique. IV. Étude du complexe de Witten, Comm. Partial Differential Equations, Volume 10 (1985) no. 3, pp. 245-340
[22] Transversalité, courants et théorie de Morse, Éditions de l’École Polytechnique, Palaiseau, 2012, x+182 pages (Un cours de topologie différentielle. [A course of differential topology],)
[23] On contact Anosov flows, Ann. of Math. (2), Volume 159 (2004) no. 3, pp. 1275-1312
[24] A current approach to Morse and Novikov theories, Rend. Mat. Appl. (7), Volume 36 (2015) no. 3-4, pp. 95-195
[25] Topics in dynamics. I: Flows, Mathematical Notes, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1969, iii+118 pages
[26] Geometric theory of dynamical systems, Springer-Verlag, New York-Berlin, 1982, xii+198 pages (An introduction, Translated from the Portuguese by A. K. Manning)
[27] Théorie des distributions, Publications de l’Institut de Mathématique de l’Université de Strasbourg, No. IX-X., Hermann, Paris, 1966, xiii+420 pages
[28] Morse inequalities for a dynamical system, Bull. Amer. Math. Soc., Volume 66 (1960), pp. 43-49
[29] Sur une partition en cellules associée à une fonction sur une variété, C. R. Acad. Sci. Paris, Volume 228 (1949), pp. 973-975
[30] Quasi-compactness of transfer operators for contact Anosov flows, Nonlinearity, Volume 23 (2010) no. 7, pp. 1495-1545
[31] Contact Anosov flows and the Fourier-Bros-Iagolnitzer transform, Ergodic Theory Dynam. Systems, Volume 32 (2012) no. 6, pp. 2083-2118
[32] The Morse-Witten complex via dynamical systems, Expo. Math., Volume 24 (2006) no. 2, pp. 127-159
[33] Supersymmetry and Morse theory, J. Differential Geom., Volume 17 (1982) no. 4, p. 661-692 (1983)
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