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Volumn 222, Issue 1, 2001, Pages 201-227

On quantum ergodicity for linear maps of the torus

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EID: 0035536274     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200100501     Document Type: Article
Times cited : (52)

References (23)
  • 1
    • 0001248604 scopus 로고
    • On the large sieve
    • 1. Bombieri E.: On the large sieve. Mathematika 12, 201-225 (1965)
    • (1965) Mathematika , vol.12 , pp. 201-225
    • Bombieri, E.1
  • 2
    • 0001920949 scopus 로고    scopus 로고
    • Equipartition of the eigenfunctions of quantized ergodic maps on the torus
    • 2. Bouzouina, A. and De Bièvre, S.: Equipartition of the eigenfunctions of quantized ergodic maps on the torus. Commun. Math. Phys. 178, 83-105 (1996)
    • (1996) Commun. Math. Phys. , vol.178 , pp. 83-105
    • Bouzouina, A.1    De Bièvre, S.2
  • 3
    • 14944371344 scopus 로고
    • Ergodicité et fonctions propres du laplacien
    • 3. Colin de Verdière, Y.: Ergodicité et fonctions propres du laplacien. Commun. Math. Phys. 102, 497-502 (1985)
    • (1985) Commun. Math. Phys. , vol.102 , pp. 497-502
    • Colin De Verdière, Y.1
  • 4
    • 0000089317 scopus 로고
    • Quantization of the orientation preserving automorphisms of the torus
    • 4. Degli Esposti, M.: Quantization of the orientation preserving automorphisms of the torus. Ann. Inst. Poincaré 58, 323-341 (1993)
    • (1993) Ann. Inst. Poincaré , vol.58 , pp. 323-341
    • Degli Esposti, M.1
  • 5
    • 34249758844 scopus 로고
    • Classical limit of the quantized hyperbolic toral automorphisms
    • 5. Degli Esposti, M., Graffi, S. and Isola, S.: Classical limit of the quantized hyperbolic toral automorphisms. Commun. Math. Phys. 167, 471-507 (1995)
    • (1995) Commun. Math. Phys. , vol.167 , pp. 471-507
    • Degli Esposti, M.1    Graffi, S.2    Isola, S.3
  • 7
    • 0003332429 scopus 로고
    • Harmonic analysis in phase space
    • Princeton, NJ: Princeton University Press
    • 7. Folland, G.: Harmonic analysis in phase space. Annals of Mathematics Studies 122, Princeton, NJ: Princeton University Press, 1989
    • (1989) Annals of Mathematics Studies , Issue.122
    • Folland, G.1
  • 8
    • 84971137261 scopus 로고
    • On the number of primes p for which p + a has a large prime factor
    • 8. Goldfeld, M.: On the number of primes p for which p + a has a large prime factor. Mathematika 16, 23-27 (1969)
    • (1969) Mathematika , vol.16 , pp. 23-27
    • Goldfeld, M.1
  • 9
    • 84956071876 scopus 로고
    • Quantisation of linear maps on a torus - Fresnel diffraction by a periodic grating
    • 9. Hannay, J.H. and Berry, M.V.: Quantisation of linear maps on a torus - Fresnel diffraction by a periodic grating. Physica D 1, 267-291 (1980)
    • (1980) Physica D , vol.1 , pp. 267-291
    • Hannay, J.H.1    Berry, M.V.2
  • 12
    • 84897987451 scopus 로고
    • On Artin's conjecture
    • 12. Hooley, C.: on Artin's conjecture. J. reine angew. Math. 225, 209-220 (1967)
    • (1967) J. Reine Angew. Math. , vol.225 , pp. 209-220
    • Hooley, C.1
  • 13
    • 0001318237 scopus 로고
    • On the quantisation of Arnold's cat
    • 13. Knabe, S.: On the quantisation of Arnold's cat. J. Phys. A: Math. Gen. 23, 2013-2025 (1990)
    • (1990) J. Phys. A: Math. Gen. , vol.23 , pp. 2013-2025
    • Knabe, S.1
  • 14
    • 0002273985 scopus 로고    scopus 로고
    • Hecke theory and equidistribution for the quantization of linear maps of the torus
    • 14. Kurlberg, P. and Rudnick, Z.: Hecke theory and equidistribution for the quantization of linear maps of the torus. Duke Math. J. 103, 47-78 (2000)
    • (2000) Duke Math. J. , vol.103 , pp. 47-78
    • Kurlberg, P.1    Rudnick, Z.2
  • 15
    • 0034554538 scopus 로고    scopus 로고
    • Quantum unique ergodicity for parabolic maps
    • 15. Marklof, J. and Rudnick, Z.: Quantum unique ergodicity for parabolic maps. Geom. and Func. Anal. 10, 1554-1578 (2000)
    • (2000) Geom. and Func. Anal. , vol.10 , pp. 1554-1578
    • Marklof, J.1    Rudnick, Z.2
  • 17
    • 0003106775 scopus 로고
    • Artin's conjecture for primitive roots
    • 17. Murty, M.: Artin's conjecture for primitive roots. Math. Intelligencer 10, no. 4, 59-67 (1988)
    • (1988) Math. Intelligencer , vol.10 , Issue.4 , pp. 59-67
    • Murty, M.1
  • 18
    • 0001022947 scopus 로고
    • Ergodic properties of eigenfunctions
    • 18. Schnirelman, A.: Ergodic properties of eigenfunctions. Usp. Math. Nauk 29, 181-182 (1974)
    • (1974) Usp. Math. Nauk , vol.29 , pp. 181-182
    • Schnirelman, A.1
  • 20
    • 0002753120 scopus 로고
    • Das asymptotische Verhalten von Summen über multiplikative Funktionen
    • 20. Wirsing, E.: Das asymptotische Verhalten von Summen über multiplikative Funktionen. Math. Ann. 143, 75-102 (1961)
    • (1961) Math. Ann. , vol.143 , pp. 75-102
    • Wirsing, E.1
  • 21
    • 84972564374 scopus 로고
    • Uniform distribution of eigenfunctions on compact hyperbolic surfaces
    • 21. Zelditch, S.: Uniform distribution of eigenfunctions on compact hyperbolic surfaces. Duke Math. J. 55, 919-941 (1987)
    • (1987) Duke Math. J. , vol.55 , pp. 919-941
    • Zelditch, S.1
  • 22
    • 0030550843 scopus 로고    scopus 로고
    • Quantum ergodicity of C*-dynamical systems
    • 22. Zelditch, S. Quantum ergodicity of C*-dynamical systems. Commun. Math. Phys. 177, 507-528 (1996)
    • (1996) Commun. Math. Phys. , vol.177 , pp. 507-528
    • Zelditch, S.1
  • 23
    • 0031513741 scopus 로고    scopus 로고
    • Index and dynamics of quantized contact transformations
    • 23. Zelditch, S.: Index and dynamics of quantized contact transformations. Ann. Inst. Fourier (Grenoble) 47, 305-363 (1997)
    • (1997) Ann. Inst. Fourier (Grenoble) , vol.47 , pp. 305-363
    • Zelditch, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.