Fetching the paper…
Reading the bibliography…
We define Pollicott-Ruelle resonances for geodesic flows on noncompact asymptotically hyperbolic negatively curved manifolds, as well as for more general open hyperbolic systems related to Axiom A flows.
Steven Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73
1967
Earlier work this paper cites.
Richard Bishop and Barrett O’Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc. 145
1969
Earlier work this paper cites.
Grigory Margulis, Certain applications of ergodic theory to the investigation of manifolds of negative curvature, Funct. Anal. Appl. 3
1969
Earlier work this paper cites.
Charles Conley and Robert Easton, Isolated invariant sets and isolating blocks, Trans. Amer. Math. Soc. 158
1971
Earlier work this paper cites.
Michael Blank, Gerhard Keller, and Carlangelo Liverani, Ruelle–Perron–Frobenius spectrum for Anosov maps, Nonlinearity 15
1973
Earlier work this paper cites.
Rufus Bowen and David Ruelle, The ergodic theory of Axiom A flows, Invent. Math. 29
1975
Earlier work this paper cites.
David Ruelle, Zeta functions for expanding maps and Anosov flows, Invent. Math. 34
1976
Earlier work this paper cites.
Rufus Bowen and Brian Marcus, Unique ergodicity for horocycle foliations, Israel J. Math. 26
1977
Earlier work this paper cites.
Victor Guillemin, Lectures on spectral theory of elliptic operators, Duke Math. J. 44
1977
Earlier work this paper cites.
Victor Guillemin and David Schaeffer, On a certain class of Fuchsian partial differential equations, Duke Math. J. 44
1977
Earlier work this paper cites.
Clark Robinson, Structural stability on manifolds with boundary, J. Diff. Eq. 37
1980
Earlier work this paper cites.
William Parry and Mark Pollicott, An analogue of the prime number theorem for closed orbits of Axiom A flows, Ann. of Math. (2) 118
1983
Earlier work this paper cites.
Mark Pollicott, On the rate of mixing of Axiom A flows, Invent. Math. 81
1985
Earlier work this paper cites.
Mark Pollicott, Meromorphic extensions of generalized zeta functions, Invent. Math. 85
1986
Earlier work this paper cites.
David Ruelle, Resonances of chaotic dynamical systems, Phys. Rev. Lett. 56
1986
Earlier work this paper cites.
Rafe Mazzeo and Richard Melrose, Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature, J. Funct. Anal. 75
1987
Earlier work this paper cites.
Calvin Moore, Exponential decay of correlation coefficients for geodesic flows, in Group representations, ergodic theory, operator algebras, and mathematical physics (Berkeley, 1984), 163–181, MSRI Publ. 6
1987
Earlier work this paper cites.
Marina Ratner, The rate of mixing for geodesic and horocycle flows, Erg. Theory Dyn. Syst. 7
1987
Earlier work this paper cites.
David Ruelle, Resonances for Axiom A flows, J. Diff. Geom. 25
1987
Earlier work this paper cites.
Lars Hörmander, The Analysis of Linear Partial Differential Operators I. Distribution Theory and Fourier Analysis, Springer, 1990
1990
Cited alongside, same era.
William Parry and Mark Pollicott, Zeta functions and the periodic orbit structure of hyperbolic dynamics, Asterisque 187–188
1990
Cited alongside, same era.
Hans Rugh, The correlation spectrum for hyperbolic analytic maps, Nonlinearity 5
1992
Cited alongside, same era.
Richard Melrose, Spectral and scattering theory for the Laplacian on asymptotically Euclidean spaces, in Spectral and scattering theory, (M. Ikawa, ed.), Marcel Dekker, 1994
1994
Cited alongside, same era.
David Fried, Meromorphic zeta functions for analytic flows, Comm. Math. Phys. 174
1995
Cited alongside, same era.
Oliver Butterley and Carlangelo Liverani, Smooth Anosov flows: correlation spectra and stability, J. Mod. Dyn. 1
2007
Later among the works it cites.
Frédéric Faure, Prequantum chaos: resonances of the prequantum cat map, J. Mod. Dyn. 1
2007
Later among the works it cites.
Frédéric Faure, Nicolas Roy, and Johannes Sjöstrand, A semiclassical approach for Anosov diffeomorphisms and Ruelle resonances, Open Math. J. 1
2008
Later among the works it cites.
Ira Herbst and Erik Skibsted, Absence of quantum states corresponding to unstable classical channels, Ann. Henri Poincaré 9
2008
Later among the works it cites.
Stéphane Nonnenmacher and Maciej Zworski, Quantum decay rates in chaotic scattering, Acta Math. 203
2009
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Wilhelm Klingenberg, Riemannian geometry, Walter de Gruyter, 1995
1995
Cited alongside, same era.
Hans Rugh, Generalized Fredholm determinants and Selberg zeta functions for Axiom A dynamical systems, Erg. Theory Dyn. Syst. 16
1996
Cited alongside, same era.
Anatole Katok and Boris Hasselblatt, Introduction to the modern theory of dynamical systems, Cambridge Univ. Press, 1997
1997
Cited alongside, same era.
Nikolai Chernov, Markov approximations and decay of correlations for Anosov flows, Ann. of Math. (2) 147
1998
Cited alongside, same era.
Dmitry Dolgopyat, On decay of correlations in Anosov flows, Ann. of Math. (2) 147
1998
Cited alongside, same era.
Alexey Kitaev, Fredholm determinants for hyperbolic diffeomorphisms of finite smoothness, Nonlinearity 12
1999
Cited alongside, same era.
Andrew Hassell, Richard Melrose, and András Vasy, Spectral and scattering theory for symbolic potentials of order zero, Adv. Math. 181
2004
Cited alongside, same era.
Frédéric Faure and Johannes Sjöstrand, Upper bound on the density of Ruelle resonances for Anosov flows, Comm. Math. Phys. 308
2011
Later among the works it cites.
Luchezar Stoyanov, Spectra of Ruelle transfer operators for Axiom A flows, Nonlinearity 24
2011
Later among the works it cites.
Maciej Zworski, Semiclassical analysis, Graduate Studies in Mathematics 138
2012
Later among the works it cites.
Frédéric Faure and Masato Tsujii, Band structure of the Ruelle spectrum of contact Anosov flows, Comptes Rendus – Mathématique 351
2013
Later among the works it cites.
Paolo Giulietti, Carlangelo Liverani, and Mark Pollicott, Anosov flows and dynamical zeta functions, Ann. of Math. (2) 178
2013
Later among the works it cites.
Luchezar Stoyanov, Pinching conditions, linearization and regularity of Axiom A flows, Discrete Cont. Dyn. Syst. 33
2013
Later among the works it cites.
Luchezar Stoyanov, Ruelle operators and decay of correlations for contact Anosov flows, C. R. Acad. Sci. Paris, Ser. I 351
2013
Later among the works it cites.
András Vasy, Microlocal analysis of asymptotically hyperbolic and Kerr–de Sitter spaces, with an appendix by Semyon Dyatlov, Invent. Math. 194
2013
Later among the works it cites.
Kiril Datchev, Semyon Dyatlov, and Maciej Zworski, Sharp polynomial bounds on the number of Pollicott–Ruelle resonances, Erg. Theory Dyn. Syst. 34
2014
Closest in time.
Semyon Dyatlov, Frédéric Faure, and Colin Guillarmou, Power spectrum of the geodesic flow on hyperbolic manifolds, Analysis&PDE 8
2015
Closest in time.
Semyon Dyatlov and Maciej Zworski, Stochastic stability of Pollicott–Ruelle resonances, Nonlinearity 28
2015
Closest in time.
Stéphane Nonnenmacher and Maciej Zworski, Decay of correlations in normally hyperbolic trapping, Invent. Math. 200
2015
Closest in time.
Masato Tsujii, Contact Anosov flows and the Fourier–Bros–Iagolnitzer transform, Erg. Theory Dyn. Syst. 32
2083
Closest in time.