Fetching the paper…
Reading the bibliography…
For Anosov flows preserving a smooth measure on a closed manifold $\mathcal{M}$, we define a natural self-adjoint operator $\Pi$ which maps into the space of invariant distributions in $\cap_{u<0} H^{u}(\mathcal{M})$ and whose kernel is made of coboundaries in $\cup_{s>0} H^{s}(\mathcal{M})$.
D. V. Anosov, Geodesic flows on closed Riemannian manifolds with negative curvature , Trudy Mat. Inst. Steklov. 90
1967
Earlier work this paper cites.
L. Hörmander, On the existence and the regularity of solutions of linear pseudo-differential equations , Enseignement Math. (2) 17
1971
Earlier work this paper cites.
M. Blank, M.G. Keller, C. Liverani, Ruelle-Perron-Frobenius spectrum for Anosov maps. Nonlinearity 15
1973
Earlier work this paper cites.
W. Klingenberg, Manifolds with geodesic flow of Anosov type , Ann. of Math 99
1974
Earlier work this paper cites.
V. Guillemin, D. Kazhdan, Some inverse spectral results for negatively curved 2 2 -manifolds. Topology 19
1980
Earlier work this paper cites.
V. Guillemin, D. Kazhdan, Some inverse spectral results for negatively curved n n - manifolds , Geometry of the Laplace operator (Proc. Sympos. Pure Math., Univ. Hawaii, Honolulu, Hawaii, 1979), pp. 153-180, Proc. Sympos. Pure Math., XXXVI, Amer. Math. Soc., Providence, R.I., 1980, MR0573432, Zbl 0456.58031
1980
Earlier work this paper cites.
M. Reed, B. Simon, Methods of modern mathematical physics. I. Functional analysis. Second edition. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, 1980. 400 pp, MR0751959, Zbl 0459.46001
1980
Earlier work this paper cites.
R. de la Llave, J.M. Marco, R. Moriyón, Canonical perturbation theory of Anosov systems and regularity results for the Livsic cohomology equation. Ann. of Math. (2) 123
1986
Earlier work this paper cites.
J-L. Journé, On a Regularity Problem Occurring in Connection with Anosov Diffeomorphisms. Comm. Math. Phys. 106
1986
Earlier work this paper cites.
L. Hörmander, The Analysis of Linear Partial Differential Operators I. Distribution Theory and Fourier Analysis, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 256. Springer-Verlag, Berlin, 1990. xii+440 pp, MR1065993, Zbl 0712.35001
1990
Earlier work this paper cites.
S. Hurder, A. Katok, Differentiability, rigidity and Godbillon-Vey classes for Anosov flows . Inst. Hautes Etudes Sci. Publ. Math. 72
1990
Earlier work this paper cites.
K. Burns, A. Katok, Infinitesimal Lyapunov functions, invariant cone families and stochastic properties of smooth dynamical systems , Erg. Th. Dyn. Sys. 14
1994
Cited alongside, same era.
A. Grigis, J. Sjöstrand, Microlocal analysis for differential operators: an introduction,
1994
Cited alongside, same era.
A. Katok, B. Hasselblatt, Modern theory of dynamical systems , With a supplementary chapter by Katok and Leonardo Mendoza. Encyclopedia of Mathematics and its Applications, 54. Cambridge University Press, Cambridge, 1995. 802 pp, MR1326374, Zbl 0878.58019
1995
Cited alongside, same era.
C. Croke, V.A. Sharafutdinov, Spectral rigidity of a compact negatively curved manifold . Topology 37
1998
Cited alongside, same era.
F.G. Friedlander, M.S. Joshi, Introduction to the theory of distributions , Cambridge Univ. Press. (1999) pp 188. MR1721032
1999
V. Sharafutdinov, M. Skokan, G. Uhlmann, Regularity of ghosts in tensor tomography. J. Geom. Anal. 15
2005
Later among the works it cites.
N. Anantharaman, S. Zelditch, Patterson–Sullivan distributions and quantum ergodicity, Ann. Henri Poincaré 8
2007
Later among the works it cites.
V. Baladi, M. Tsujii, Anisotropic Hölder and Sobolev spaces for hyperbolic diffeomorphisms. Ann. Inst. Fourier 57
2007
Later among the works it cites.
O. Butterley, C. Liverani, Smooth Anosov flows: correlation spectra and stability. J. Mod. Dyn. 1
2007
Later among the works it cites.
F. Faure, J. Sjöstrand, Upper bound on the density of Ruelle resonances for Anosov flows, Comm. Math. Phys. 308
2011
Later among the works it cites.
M. Zworski, Semiclassical analysis, Graduate Studies in Mathematics 138
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.
G.P. Paternain, Geodesic flows , Progress in Mathematics 180, Birkhäuser Boston, Inc., Boston, MA, 1999. xiv+149 pp, MR1712465, Zbl 0930.53001
1999
Cited alongside, same era.
N.S. Dairbekov, V.A. Sharafutdinov, Some problems of integral geometry on Anosov manifolds , Erg. Th. and Dyn. Sys. 23
2003
Cited alongside, same era.
C. Liverani, On contact Anosov flows. Ann. of Math. (2) 159
2004
Cited alongside, same era.
S. Gouëzel, C. Liverani, Banach spaces adapted to Anosov systems. Erg. Th. Dyn. Sys. 26
2005
Cited alongside, same era.
L. Pestov, G. Uhlmann, Two dimensional compact simple Riemannian manifolds are boundary distance rigid. Ann. of Math. (2) 161
2005
Cited alongside, same era.
S. Dyatlov, M. Zworski, Dynamical zeta functions for Anosov flows via microlocal analysis , to appear in Ann. Sci. Ec. Norm. Supér. arXiv: 1306.4203,
Cited in the paper.
S. Dyatlov, M. Zworski, Mathematical theory of scattering resonances , book in preparation. Available at http://math.mit.edu/ ∼ \sim dyatlov/res/res.pdf
Cited in the paper.
2012
Later among the works it cites.
G.P. Paternain, M. Salo, G. Uhlmann, Tensor tomography on surfaces. Invent. Math. 193
2013
Later among the works it cites.
A. Vasy, Microlocal analysis of asymptotically hyperbolic and Kerr-de Sitter spaces , with an appendix by Semyon Dyatlov, Inventiones Math 194
2013
Later among the works it cites.
G.P. Paternain, M. Salo, G. Uhlmann, Spectral rigidity and invariant distributions on Anosov surfaces. J. Diff. Geom. 98
2014
Closest in time.
G. Uhlmann, A. Vasy, The inverse problem for the local geodesic ray transform , preprint arXiv: 1210.2084
2084
Closest in time.