@article{AIHPA_1998__69_1_1_0, author = {De Bi\`evre, S. and Degli Esposti, M.}, title = {Egorov theorems and equidistribution of eigenfunctions for the quantized sawtooth and {Baker} maps}, journal = {Annales de l'I.H.P. Physique th\'eorique}, pages = {1--30}, publisher = {Gauthier-Villars}, volume = {69}, number = {1}, year = {1998}, mrnumber = {1635807}, zbl = {0922.58074}, language = {en}, url = {http://www.numdam.org/item/AIHPA_1998__69_1_1_0/} }
TY - JOUR AU - De Bièvre, S. AU - Degli Esposti, M. TI - Egorov theorems and equidistribution of eigenfunctions for the quantized sawtooth and Baker maps JO - Annales de l'I.H.P. Physique théorique PY - 1998 SP - 1 EP - 30 VL - 69 IS - 1 PB - Gauthier-Villars UR - http://www.numdam.org/item/AIHPA_1998__69_1_1_0/ LA - en ID - AIHPA_1998__69_1_1_0 ER -
%0 Journal Article %A De Bièvre, S. %A Degli Esposti, M. %T Egorov theorems and equidistribution of eigenfunctions for the quantized sawtooth and Baker maps %J Annales de l'I.H.P. Physique théorique %D 1998 %P 1-30 %V 69 %N 1 %I Gauthier-Villars %U http://www.numdam.org/item/AIHPA_1998__69_1_1_0/ %G en %F AIHPA_1998__69_1_1_0
De Bièvre, S.; Degli Esposti, M. Egorov theorems and equidistribution of eigenfunctions for the quantized sawtooth and Baker maps. Annales de l'I.H.P. Physique théorique, Tome 69 (1998) no. 1, pp. 1-30. http://www.numdam.org/item/AIHPA_1998__69_1_1_0/
[1] Ergodic Problems in Classical Mechanics, Benjamin, New York, 1968. | MR | Zbl
, ,[2] The Quantized Baker's Transformation, Annals of Physics, Vol. 190, 1989, 1-31. | MR | Zbl
, ,[3] Equipartition of the eigenfunctions of quantized ergodic maps on the torus, Commun. Math. Phys., Vol. 178, 1996, 83-105. | MR | Zbl
, ,[4] Quantization of Anosov maps, Annals of Physics, Vol. 237, 1, 1995, 46-65. | MR | Zbl
and ,[5] Construction de la paramétrix du problème mixte hyperbolique pour l'équation d'ondes, C. R. Acad. Sci. Paris, Vol. 276, 1973, 1213-1215. | MR | Zbl
,[6] Ergodic and statistical properties of piecewise linear hyperbolic automorphisms of the two-torus, J. Stat. Phys., Vol. 69, 1992, 111-134. | MR | Zbl
,[7] Ergodicité et functions propres du Laplacien, Commun. Math. Phys., Vol. 102, 1985, 497-502. | MR | Zbl
,[8] Distribution of matrix elements and level spacings for classical chaotic systems, Ann. Inst. H. Poincaré, Vol. 61, 4, 1994, 443-483. | Numdam | MR | Zbl
, ,[9] Quantization of a class of piecewise affine transformations on the torus, Commun. Math. Phys., Vol. 176, 1995, 73-94. | MR | Zbl
, and ,[10] Quantization of the orientation preserving automorphisms of the torus, Ann. Inst. Henri Poincaré, Vol. 58, 1993, 323-341. | Numdam | MR | Zbl
,[11] Classical limit of the quantized hyperbolic toral automorphisms, Commun. Math. Phys., Vol. 167, 1995, 471-507. | MR | Zbl
, and ,[12] A modern Introduction. Volume 1, Graduate Text in Mathematics, Vol. 64, 1979. | Zbl
, Fourier Series.[13] Egorov's theorem on a manifold with diffractive boundary, Comm. P. D. E., Vol. 6, 6, 1981, 651-687. | MR | Zbl
,[14] Ergodic properties of eigenfunctions for the Dirichlet problem, Duke Math. Jour., Vol. 71, 1993, 559-607. | MR | Zbl
, ,[15] Quantization of linear maps on a torus - Fresnel diffraction by a periodic grating, Physica D, Vol. 1, 1980, 267-291. | MR
, ,[16] Optical realization of the baker's transformation, Nonlinearity, Vol. 7, 1994, 1327-1342 | MR | Zbl
, , ,[17] Ergodicité et limite semi-classique, Commun. Math. Phys., Vol. 131, 1985, 493-520.
, A.MARTINEZ, ,[18] Ph. D. thesis University of Bristol, 1989.
,[19] The cat maps: quantum mechanics and classical motion, Nonlinearity, Vol. 4, 1991, 309-341. | MR | Zbl
,[20] Semiclassical theory of the Sawtooth map, Phys. Lett. A, Vol. 192, 1994, 345-354. | MR | Zbl
,[21] Decay of correlations, Annals of Mathematics, Vol. 142, 1995, 239-301. | MR | Zbl
,[22] Ergodicity in Hamiltonian systems, to appear in Dyn. Rep., Vol. 4. | MR
, ,[23] Semiclassical dynamics in the strongly chaotic regime: breaking the log-time barrier, Physica D, Vol. 55, 1992, 340-357. | MR | Zbl
, , ,[24] Autour de l'approximation semi-classique, Birkhaüser Boston, 1987. | MR | Zbl
,[25] Arithmetic quantum chaos, Tel Aviv Lectures, 1993.
,[26] Classical structures in the quantized Baker transformation, Annals of Physics, Vol. 199, 1990, 37-60. | MR | Zbl
,[27] Towards a semiclassical theory of the quantum baker's map, Physica D, Vol. 79, 1994, 206-268. | MR | Zbl
, ,[28] The quantized D-transformation, (preprint 1995). | MR
, ,[29] Ergodic properties of the discontinuous sawtooth map, J. Stat. Phys., Vol. 67, 1992, 251. | MR | Zbl
,[30] Uniform distribution of eigenfunctions on compact hyperbolic surfaces, Duke Math. Jour., 55, 1987, 919-941. | MR | Zbl
,[3 1 ] Quantum transition amplitudes for ergodic and completely integrable systems, Journ. Funct. Ana., Vol. 94, 1990, 415-436. | MR | Zbl
,[32] Quantum ergodicity of C* dynamical systems, Commun. Math. Phys., Vol. 177, 1996, 507-528. | MR | Zbl
,[33] Index and dynamics of quantized contact transformations, Ann. Inst. Fourier, Vol. 47, 1997, 305-363. | Numdam | MR | Zbl
,[34] Ergodicity of eigenfunctions for ergodic billiards, Commun. Math. Phys., Vol. 175, 1996, 3, 673-682. | MR | Zbl
, ,