메뉴 건너뛰기




Volumn 168, Issue 2, 2008, Pages 435-475

Entropy and the localization of eigenfunctions

Author keywords

[No Author keywords available]

Indexed keywords


EID: 57849105880     PISSN: 0003486X     EISSN: None     Source Type: Journal    
DOI: 10.4007/annals.2008.168.435     Document Type: Article
Times cited : (119)

References (24)
  • 1
    • 2442509621 scopus 로고    scopus 로고
    • On the zero-temperature or vanishing viscosity limit for cer-tain Markov processes arising from Lagrangian dynamics
    • N. Anantharaman, On the zero-temperature or vanishing viscosity limit for cer-tain Markov processes arising from Lagrangian dynamics, J. Eur. Math. Soc. (JEMS) 6 (2004), 207-276.
    • (2004) J. Eur. Math. Soc. (JEMS) , vol.6 , pp. 207-276
    • Anantharaman, N.1
  • 2
    • 71249093107 scopus 로고    scopus 로고
    • Semi-classical entropy of the Walsh-quantized baker's map, preprint
    • N. Anantharaman and S. Nonnenmacher, Semi-classical entropy of the Walsh-quantized baker's map, preprint.
    • Anantharaman, N.1    Nonnenmacher, S.2
  • 3
    • 0002946916 scopus 로고
    • Equivalence of uniform hyperbolicity for symplectic twist maps and phonon gap for Frenkel-Kontorova models
    • S. Aubry, R. S. McKay, and C. Baesens, Equivalence of uniform hyperbolicity for symplectic twist maps and phonon gap for Frenkel-Kontorova models, Physica D 56 (1992), 123-134.
    • (1992) Physica D , vol.56 , pp. 123-134
    • Aubry, S.1    McKay, R.S.2    Baesens, C.3
  • 4
    • 0001319171 scopus 로고
    • On the wave equation on a compact Riemannian manifold without conjugate points
    • P. Berard, On the wave equation on a compact Riemannian manifold without conjugate points, Math. Z. 155 (1977), 249-276.
    • (1977) Math. Z. , vol.155 , pp. 249-276
    • Berard, P.1
  • 5
    • 0037534326 scopus 로고    scopus 로고
    • Controlling strong scarring for quantized ergodic toral automorphisms
    • F. Bonechi and S. De Biévre, Controlling strong scarring for quantized ergodic toral automorphisms, Duke Math. J. 117 (2003), 571-587.
    • (2003) Duke Math. J. , vol.117 , pp. 571-587
    • Bonechi, F.1    De Biévre, S.2
  • 7
    • 0036487116 scopus 로고    scopus 로고
    • Uniform semiclassical estimates for the propagation of quantum observables
    • A. Bouzouina and D. Robert, Uniform semiclassical estimates for the propagation of quantum observables, Duke Math. J. 111 (2002), 223-252.
    • (2002) Duke Math. J. , vol.111 , pp. 223-252
    • Bouzouina, A.1    Robert, D.2
  • 8
    • 14944371344 scopus 로고
    • Ergodicité et fonctions propres du laplacien
    • Y. Colin de Verdiére, Ergodicité et fonctions propres du laplacien, Comm. Math. Phys. 102 (1985), 497-502.
    • (1985) Comm. Math. Phys. , vol.102 , pp. 497-502
    • Colin de Verdiére, Y.1
  • 10
    • 0042417242 scopus 로고    scopus 로고
    • Scarred eigenstates for quantum cat maps of minimal periods
    • F. Faure, N. Nonnenmacher, and S. De Biévre, Scarred eigenstates for quantum cat maps of minimal periods, Comm. Math. Phys. 239 (2003), 449-492.
    • (2003) Comm. Math. Phys. , vol.239 , pp. 449-492
    • Faure, F.1    Nonnenmacher, N.2    De Biévre, S.3
  • 11
    • 1542718367 scopus 로고    scopus 로고
    • On the maximal scarring for quantum cat map eigenstates
    • F. Faure and N. Nonnenmacher, On the maximal scarring for quantum cat map eigenstates, Comm. Math. Phys. 245 (2004), 201-214.
    • (2004) Comm. Math. Phys. , vol.245 , pp. 201-214
    • Faure, F.1    Nonnenmacher, N.2
  • 15
    • 0001048955 scopus 로고
    • The metric entropy of di eomorphisms. I. Char-acterization of measures satisfying Pesin's entropy formula
    • F. Ledrappier and L.-S. Young, The metric entropy of di eomorphisms. I. Char-acterization of measures satisfying Pesin's entropy formula, Ann. of Math. 122 (1985), 509-539.
    • (1985) Ann. of Math. , vol.122 , pp. 509-539
    • Ledrappier, F.1    Young, L.-S.2
  • 16
    • 33644586868 scopus 로고    scopus 로고
    • Invariant measures and arithmetic quantum unique ergodicity
    • E. Lindenstrauss, Invariant measures and arithmetic quantum unique ergodicity, Ann. of Math. 163 (2006), 165-219.
    • (2006) Ann. of Math. , vol.163 , pp. 165-219
    • Lindenstrauss, E.1
  • 17
    • 21344499327 scopus 로고
    • The behaviour of eigenstates of arithmetic hyperbolic manifolds
    • Z. Rudnick and P. Sarnak, The behaviour of eigenstates of arithmetic hyperbolic manifolds, Comm. Math. Phys. 161 (1994), 195-213.
    • (1994) Comm. Math. Phys. , vol.161 , pp. 195-213
    • Rudnick, Z.1    Sarnak, P.2
  • 18
    • 0000662003 scopus 로고
    • Arithmetic quantum chaos
    • (Tel Aviv)
    • P. Sarnak, Arithmetic quantum chaos, in The Schur Lectures (1992) (Tel Aviv), 183-236.
    • (1992) The Schur Lectures , pp. 183-236
    • Sarnak, P.1
  • 19
    • 71249099560 scopus 로고
    • Bar-Ilan Univ., Ramat Gan
    • Israel Math. Conf. Proc. 8, Bar-Ilan Univ., Ramat Gan, 1995.
    • (1995) Israel Math. Conf. Proc. , vol.8
  • 20
    • 0141457360 scopus 로고    scopus 로고
    • Spectra of hyperbolic surfaces
    • P. Sarnak, Spectra of hyperbolic surfaces, Bull. Amer. Math. Soc. 40 (2003), 441- 478.
    • (2003) Bull. Amer. Math. Soc. , vol.40 , pp. 441-478
    • Sarnak, P.1
  • 21
    • 71249119717 scopus 로고    scopus 로고
    • (see preprints/letters/papers)
    • P. Sarnak, www.math.princeton.edu/sarnak; (see preprints/letters/papers).
    • Sarnak, P.1
  • 22
    • 0001022947 scopus 로고
    • Ergodic properties of eigenfunctions (Russe)
    • A. I. Snirelman, Ergodic properties of eigenfunctions (Russe), Uspehi Mat. Nauk. 29 (1974), 181-182.
    • (1974) Uspehi Mat. Nauk. , vol.29 , pp. 181-182
    • Snirelman, A.I.1
  • 23
    • 38249039021 scopus 로고
    • Pseudodierential analysis on hyperbolic surfaces
    • S. Zelditch, Pseudodierential analysis on hyperbolic surfaces, J. Funct. Anal. 68 (1986), 72-105.
    • (1986) J. Funct. Anal. , vol.68 , pp. 72-105
    • Zelditch, S.1
  • 24
    • 84972564374 scopus 로고
    • Uniform distribution of eigenfunctions on compact hyperbolic surfaces
    • P. Sarnak, Uniform distribution of eigenfunctions on compact hyperbolic surfaces, Duke Math. J. 55 (1987), 919-941.
    • (1987) Duke Math. J. , vol.55 , pp. 919-941
    • Sarnak, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.