146
NALINI ANANTHARAMAN
(Berll)
N. BERGERON - Le spectre des surfaces hyperboliques, Savoirs Actuels, EDP
Sciences, Les Ulis; CNRS Éditions, Paris, 2011.
(BDB96) A. BOUZOUINA & S. DE BIÈVRE - « Equipartition of the eigenfunctions of
quantized ergodic maps on the torus », Comm. Math. Phys. 178 (1996),
no. 1, p. 83-105.
(EvalO)
L.- C. EVANS - Partial differential equations, 2e éd., Graduate Studies in
Mathematics, vol. 19, American Mathematical Society, Providence, RI, 2010.
(Far08)
J. FARAUT - Analysis on Lie groups. An introduction, Cambridge Studies in
Advanced Mathematics, vol. 110, Cambridge University Press, Cambridge,
2008.
(FNDB03J. F. FAURE, S. NONNENMACHER & S. DE BIÈVRE - « Scarred eigenstates for
quantum cat maps of minimal periods », Comm. Math. Phys. 239 (2003),
no. 3, p. 449-492.
(GL93)
P. GÉRARD & É. LEICHTNAM - « Ergodic properties of eigenfunctions for the
Dirichlet problem », Duke Math. J. 71 (1993), no. 2, p. 559-607.
(HaslO)
A. HASSELL - « Ergodic billiards that are not quantum unique ergodic », Ann.
of Math. (2) 171 (2010), no. 1, p. 605-619.
(Hej76)
D. A. HEJHAL - The Selbery trace formula for PSL(2, R). Vol. I, Lecture
Notes in Mathematics, Vol. 548, Springer-Verlag, Berlin-New York, 1976.
(Hux02)
M. N. HUXLEY - « Integer points, exponential sums and the Riemann zeta
function », in Number theory for the millennium, II (Urbana, IL, 2000}, A
K Peters, Natick, MA, 2002, p. 275-290.
(Jak97)
D. JAKOBSON - «Quantum limits on fiat tori », Ann. of Math. (2) 145 (1997),
no. 2, p. 235-266.
(Lin06)
E. LINDENSTRAUSS - « Invariant measures and arithmetic quantum unique
ergodicity », Ann. of Math. (2) 163 (2006), no. 1, p. 165-219.
(MaclO)
F. MACIÀ - « High-frequency propagation for the Schrodinger equation on
the torus », J. Pu.net. Anal. 258 (2010), no. 3, p. 933-955.
(Nas56)
J. NASH - «The imbedding problem for Riemannian manifolds», Ann. of
Math. (2) 63 (1956), p. 2o-63.
(RS94)
Z. RUDNICK & P. SARNAK - « The behaviour of eigenstates of arithmetic
hyperbolic manifolds», Comm. Math. Phys. 161 (1994), no. 1, p. 195-213.
(Sar03)
P. SARNAK - « Spectra of hyperbolic surfaces», Bull. Amer. Math. Soc.
(N.S.) 40 (2003), no. 4, p. 441-478.
(Sarll)
___ , « Recent progress on the quantum unique ergodicity conjecture»,
Bull. Amer. Math. Soc. (N.S.) 48 (2011), no. 2, p. 211-228.
(Sni74)
A. 1. SNIREL 1 MAN - « Ergodic properties of eigenfunctions », Uspehi Mat.
Nauk 29 (1974), no. 6(180), p. 181-182.
(CdV85)
Y. COLIN DE VERDIÈRE - «Ergodicité et fonctions propres du laplacien»,
Comm. Math. Phys. 102 (1985), no. 3, p. 497-502.
(Zel87)
S. ZELDITCH - « Uniform distribution of eigenfunctions on compact hyperbolic
surfaces», Duke Math. J. 55 (1987), no. 4, p. 919-941.
(Zyg74)
A. ZYGMUND - «On Fourier coefficients and transforms of functions of two
variables», Studia Math. 50 (1974), p. 189-201.
NALINI ANANTHARAMAN, Université Paris-Sud 11, Mathématiques, Bât. 425,
91405 Orsay cedex • E-mail : Nalini. Anantharaman©math. u-psud. fr
Url :http://www.math.u-psud.fr/-anantharaman/
NALINI ANANTHARAMAN
(Berll)
N. BERGERON - Le spectre des surfaces hyperboliques, Savoirs Actuels, EDP
Sciences, Les Ulis; CNRS Éditions, Paris, 2011.
(BDB96) A. BOUZOUINA & S. DE BIÈVRE - « Equipartition of the eigenfunctions of
quantized ergodic maps on the torus », Comm. Math. Phys. 178 (1996),
no. 1, p. 83-105.
(EvalO)
L.- C. EVANS - Partial differential equations, 2e éd., Graduate Studies in
Mathematics, vol. 19, American Mathematical Society, Providence, RI, 2010.
(Far08)
J. FARAUT - Analysis on Lie groups. An introduction, Cambridge Studies in
Advanced Mathematics, vol. 110, Cambridge University Press, Cambridge,
2008.
(FNDB03J. F. FAURE, S. NONNENMACHER & S. DE BIÈVRE - « Scarred eigenstates for
quantum cat maps of minimal periods », Comm. Math. Phys. 239 (2003),
no. 3, p. 449-492.
(GL93)
P. GÉRARD & É. LEICHTNAM - « Ergodic properties of eigenfunctions for the
Dirichlet problem », Duke Math. J. 71 (1993), no. 2, p. 559-607.
(HaslO)
A. HASSELL - « Ergodic billiards that are not quantum unique ergodic », Ann.
of Math. (2) 171 (2010), no. 1, p. 605-619.
(Hej76)
D. A. HEJHAL - The Selbery trace formula for PSL(2, R). Vol. I, Lecture
Notes in Mathematics, Vol. 548, Springer-Verlag, Berlin-New York, 1976.
(Hux02)
M. N. HUXLEY - « Integer points, exponential sums and the Riemann zeta
function », in Number theory for the millennium, II (Urbana, IL, 2000}, A
K Peters, Natick, MA, 2002, p. 275-290.
(Jak97)
D. JAKOBSON - «Quantum limits on fiat tori », Ann. of Math. (2) 145 (1997),
no. 2, p. 235-266.
(Lin06)
E. LINDENSTRAUSS - « Invariant measures and arithmetic quantum unique
ergodicity », Ann. of Math. (2) 163 (2006), no. 1, p. 165-219.
(MaclO)
F. MACIÀ - « High-frequency propagation for the Schrodinger equation on
the torus », J. Pu.net. Anal. 258 (2010), no. 3, p. 933-955.
(Nas56)
J. NASH - «The imbedding problem for Riemannian manifolds», Ann. of
Math. (2) 63 (1956), p. 2o-63.
(RS94)
Z. RUDNICK & P. SARNAK - « The behaviour of eigenstates of arithmetic
hyperbolic manifolds», Comm. Math. Phys. 161 (1994), no. 1, p. 195-213.
(Sar03)
P. SARNAK - « Spectra of hyperbolic surfaces», Bull. Amer. Math. Soc.
(N.S.) 40 (2003), no. 4, p. 441-478.
(Sarll)
___ , « Recent progress on the quantum unique ergodicity conjecture»,
Bull. Amer. Math. Soc. (N.S.) 48 (2011), no. 2, p. 211-228.
(Sni74)
A. 1. SNIREL 1 MAN - « Ergodic properties of eigenfunctions », Uspehi Mat.
Nauk 29 (1974), no. 6(180), p. 181-182.
(CdV85)
Y. COLIN DE VERDIÈRE - «Ergodicité et fonctions propres du laplacien»,
Comm. Math. Phys. 102 (1985), no. 3, p. 497-502.
(Zel87)
S. ZELDITCH - « Uniform distribution of eigenfunctions on compact hyperbolic
surfaces», Duke Math. J. 55 (1987), no. 4, p. 919-941.
(Zyg74)
A. ZYGMUND - «On Fourier coefficients and transforms of functions of two
variables», Studia Math. 50 (1974), p. 189-201.
NALINI ANANTHARAMAN, Université Paris-Sud 11, Mathématiques, Bât. 425,
91405 Orsay cedex • E-mail : Nalini. Anantharaman©math. u-psud. fr
Url :http://www.math.u-psud.fr/-anantharaman/