@incollection{AST_2008__317__393_0, author = {Colin de Verdi\`ere, Yves}, title = {Semi-classical measures and entropy [after {Nalini} {Anantharaman} and {St\'ephane} {Nonnenmacher]}}, booktitle = {S\'eminaire Bourbaki - Volume 2006/2007 - Expos\'es 967-981}, series = {Ast\'erisque}, note = {talk:978}, pages = {393--414}, publisher = {Soci\'et\'e math\'ematique de France}, number = {317}, year = {2008}, mrnumber = {2487740}, zbl = {1155.37020}, language = {en}, url = {http://archive.numdam.org/item/AST_2008__317__393_0/} }
TY - CHAP AU - Colin de Verdière, Yves TI - Semi-classical measures and entropy [after Nalini Anantharaman and Stéphane Nonnenmacher] BT - Séminaire Bourbaki - Volume 2006/2007 - Exposés 967-981 AU - Collectif T3 - Astérisque N1 - talk:978 PY - 2008 SP - 393 EP - 414 IS - 317 PB - Société mathématique de France UR - http://archive.numdam.org/item/AST_2008__317__393_0/ LA - en ID - AST_2008__317__393_0 ER -
%0 Book Section %A Colin de Verdière, Yves %T Semi-classical measures and entropy [after Nalini Anantharaman and Stéphane Nonnenmacher] %B Séminaire Bourbaki - Volume 2006/2007 - Exposés 967-981 %A Collectif %S Astérisque %Z talk:978 %D 2008 %P 393-414 %N 317 %I Société mathématique de France %U http://archive.numdam.org/item/AST_2008__317__393_0/ %G en %F AST_2008__317__393_0
Colin de Verdière, Yves. Semi-classical measures and entropy [after Nalini Anantharaman and Stéphane Nonnenmacher], in Séminaire Bourbaki - Volume 2006/2007 - Exposés 967-981, Astérisque, no. 317 (2008), Talk no. 978, 22 p. http://archive.numdam.org/item/AST_2008__317__393_0/
[1] Entropy and localization of eigenfunctions", to appear in Annals of Math., 2008. | Numdam | MR | Zbl
- "[2] Entropy of eigenfunctions", preprint arXiv:0704.1564, 2007. | Zbl
, & - "[3] Half-delocalization of eigenfunctions for the Laplacian on an Anosov manifold", Ann. Inst. Fourier 57 (2007), p. 2465-2523. | DOI | EuDML | Numdam | MR | Zbl
& - "[4] The eigenfunctions which are concentrated near a closed geodesic", in Problems of Mathematical Physics, No. 2, Spectral Theory, Diffraction Problems (Russian), Izdat. Leningrad. Univ., Leningrad, 1967, p. 15-25. | MR | Zbl
& - "[5] Le spectre d'une variété riemannienne, Lecture Notes in Mathematics, Vol. 194, Springer, 1971. | MR | Zbl
, & -[6] Exponential mixing and time scales in quantized hyperbolic maps on the torus", Comm. Math. Phys. 211 (2000), p. 659-686. | DOI | MR | Zbl
& - "[7] Controlling strong scarring for quantized ergodic toral automorphisms", Duke Math. J. 117 (2003), p. 571-587. | DOI | MR | Zbl
& , "[8] Equipartition of the eigenfunctions of quantized ergodic maps on the torus", Comm. Math. Phys. 178 (1996), p. 83-105. | DOI | MR | Zbl
& - "[9] Uniform semiclassical estimates for the propagation of quantum observables", Duke Math. J. 111 (2002), p. 223-252. | DOI | MR | Zbl
& - "[10] Introduction to dynamical Systems, Cambridge University Press, 2002. | DOI | MR | Zbl
& -[11] Ergodicité et fonctions propres du laplacien", Comm. Math. Phys. 102 (1985), p. 497-502. | DOI | MR | Zbl
- "[12] Équilibre instable en régime semiclassique. I. Concentration microlocale", Comm. Partial Differential Equations 19 (1994), p. 1535-1563. | DOI | MR
& - "[13] Spectral asymptotics in the semi-classical limit, London Mathematical Society Lecture Note Series, vol. 268, Cambridge University Press, 1999. | MR | Zbl
& -[14] Lectures on semiclassical analysis (v. 3)", http://math.berkeley.edu/~zworski, 2007.
& - "[15] Semi-classical formula beyond the Ehrenfest time in quantum chaos. (I) Trace formula", Ann. Inst. Fourier 57 (2007), p. 2525-2599. | DOI | EuDML | Numdam | MR | Zbl
- "[16] On the maximal scarring for quantum cat map eigenstates", Comm. Math. Phys. 245 (2004), p. 201-214. | DOI | MR | Zbl
& - "[17] Scarred eigenstates for quantum cat maps of minimal periods", Comm. Math. Phys. 239 (2003), p. 449-492. | DOI | MR | Zbl
, & - "[18] Microlocal defect measures", Comm. Partial Differential Equations 16 (1991), p. 1761-1794. | DOI | MR | Zbl
- "[19] Ergodic properties of eigenfunctions for the Dirichlet problem", Duke Math. J. 71 (1993), p. 559-607. | MR | Zbl
& - "[20] Wavepacket dynamics and quantum chaology", in Chaos et physique quantique (Les Houches, 1989), North-Holland, 1991, p. 547-664. | MR
- "[21] Introduction to the modem theory of dynamical Systems, Encyclopedia of Mathematics and its Applications, vol. 54, Cambridge University Press, 1995. | MR | Zbl
& -[22] Arithmetic quantum unique ergodicity for symplectic linear maps of the multidimensional torus", preprint arXiv:math-ph/0510079v5. | DOI | MR | Zbl
- "[23] Complementary observables and uncertainty relations", Phys. Rev. D (3) 35 (1987), p. 3070-3075. | DOI | MR
- "[24] On the projections of measures invariant under the geodesic flow", Int. Math. Res. Not. 9 (2003), p. 511-526. | DOI | MR | Zbl
& - "[25] The metric entropy of diffeomorphisms. I. Characterization of measures satisfying Pesin's entropy formula", Ann. of Math. (2) 122 (1985), p. 509-539. | DOI | MR | Zbl
& - "[26] Invariant measures and arithmetic quantum unique ergodicity", Ann. of Math. (2) 163 (2006), p. 165-219. | DOI | MR | Zbl
- "[27] Generalized entropic uncertainty relations", Phys. Rev. Lett. 60 (1988), p. 1103-1106. | DOI | MR
& - "[28] Ergodic theory and differentiable dynamics, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge, vol. 8, Springer, 1987. | MR | Zbl
-[29] Spectrum and eigenfunctions for a Hamiltonian with stochastic trajectories", Phys. Rev. Lett. 42 (1979), p. 1189-1191. | DOI
& - "[30] Wave chaos in the stadium: statistical properties of short-wave solutions of the Helmholtz equation", Phys. Rev. A (3) 37 (1988), p. 3067-3086. | DOI | MR
& , "[31] On the construction of quasimodes associated with stable periodic orbits", Comm. Math. Phys. 51 (1976), p. 219-242. | DOI | MR | Zbl
- "[32] The behaviour of eigenstates of arithmetic hyperbolic manifolds", Comm. Math. Phys. 161 (1994), p. 195-213. | DOI | MR | Zbl
& - "[33] Semiclassical behaviour of expectation values in time evolved Lagrangian states for large times", Comm. Math. Phys. 256 (2005), p. 239-254. | DOI | MR | Zbl
- "[34] Ergodic properties of eigenfunctions", Uspehi Mat. Nauk 29 (1974), p. 181-182. | MR | Zbl
- "[35] -measures, a new approach for studying homogenisation, oscillations and concentration effects in partial differential equations", Proc. Roy. Soc. Edinburgh Sect. A 115 (1990), p. 193-230. | DOI | MR | Zbl
- "[36] Uniform distribution of eigenfunctions on compact hyperbolic surfaces", Duke Math. J. 55 (1987), p. 919-941. | MR | Zbl
- "[37] Ergodicity of eigenfunctions for ergodic billiards", Comm. Math. Phys. 175 (1996), p. 673-682. | DOI | Zbl
& - "