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Volumn 146, Issue 2, 2009, Pages 253-280

Cantor spectrum for schrödinger operators with potentials arising from generalized skew-shifts

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EID: 77954016470     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/00127094-2008-065     Document Type: Article
Times cited : (55)

References (23)
  • 1
    • 62749172433 scopus 로고    scopus 로고
    • A uniform dichotomy for generic SL(2,R{double-struck}) cocycles over a minimal base
    • A. Avila and J. Bochi, A uniform dichotomy for generic SL(2,R{double-struck}) cocycles over a minimal base, Bull. Soc. Math. France 135 (2007), 407-417.
    • (2007) Bull. Soc. Math. France , vol.135 , pp. 407-417
    • Avila, A.1    Bochi, J.2
  • 2
    • 29444455718 scopus 로고    scopus 로고
    • Generic singular spectrum for ergodic Schrödinger operators
    • A. Avila and D. Damanik, Generic singular spectrum for ergodic Schrödinger operators, Duke Math. J. 130 (2005), 393-400.
    • (2005) Duke Math. J. , vol.130 , pp. 393-400
    • Avila, A.1    Damanik, D.2
  • 3
    • 0036896073 scopus 로고    scopus 로고
    • Genericity of zero Lyapunov exponents
    • J. Bochi, Genericity of zero Lyapunov exponents, Ergodic Theory Dynam. Systems 22 (2002), 1667-1696.
    • (2002) Ergodic Theory Dynam. Systems , vol.22 , pp. 1667-1696
    • Bochi, J.1
  • 4
    • 50249130697 scopus 로고    scopus 로고
    • Generic continuous spectrum for ergodic Schrödinger operators
    • M. Boshernitzan and D. Damanik, Generic continuous spectrum for ergodic Schrödinger operators, Comm. Math. Phys. 283 (2008), 647-662.
    • (2008) Comm. Math. Phys. , vol.283 , pp. 647-662
    • Boshernitzan, M.1    Damanik, D.2
  • 5
    • 0002859579 scopus 로고    scopus 로고
    • Positive Lyapounov exponents for most energies
    • Lecture Notes in Math. 1745, Springer, Berlin
    • J. Bourgain, "Positive Lyapounov exponents for most energies" in Geometric Aspects of Functional Analysis, Lecture Notes in Math. 1745, Springer, Berlin, 2000, 37-66.
    • (2000) Geometric Aspects of Functional Analysis , vol.1745 , pp. 37-66
    • Bourgain, J.1
  • 6
    • 0036433781 scopus 로고    scopus 로고
    • On the spectrum of lattice Schrödinger operators with deterministic potential
    • J. Bourgain, On the spectrum of lattice Schrödinger operators with deterministic potential, J. Anal. Math. 87 (2002), 37-75.
    • (2002) J. Anal. Math. , vol.87 , pp. 37-75
    • Bourgain, J.1
  • 7
    • 84860070594 scopus 로고    scopus 로고
    • Green's Function Estimates for Lattice Schrödinger Operators and Applications
    • Princeton Univ. Press, Princeton
    • J. Bourgain, Green's Function Estimates for Lattice Schrödinger Operators and Applications, Ann. of Math. Stud. 158, Princeton Univ. Press, Princeton, 2005.
    • (2005) Ann. of Math. Stud. , pp. 158
    • Bourgain, J.1
  • 8
    • 0035402419 scopus 로고    scopus 로고
    • Anderson localization for Schrödinger operators on Z{double-struck} with potentials given by the skew-shift
    • J. Bourgain, M. Goldstein, and W. Schlag, Anderson localization for Schrödinger operators on Z{double-struck} with potentials given by the skew-shift, Comm. Math. Phys. 220 (2001), 583-621.
    • (2001) Comm. Math. Phys. , vol.220 , pp. 583-621
    • Bourgain, J.1    Goldstein, M.2    Schlag, W.3
  • 9
    • 0040992116 scopus 로고
    • Almost periodic properties of bounded solutions of linear differential equations with almost periodic coefficients
    • R. H. Cameron, Almost periodic properties of bounded solutions of linear differential equations with almost periodic coefficients, J. Math. Phys. 15 (1936), 73-81.
    • (1936) J. Math. Phys. , vol.15 , pp. 73-81
    • Cameron, R.H.1
  • 10
    • 27844561142 scopus 로고    scopus 로고
    • A generic bounded linear cocycle has simple Lyapunov spectrum
    • N. Dinh Cong, A generic bounded linear cocycle has simple Lyapunov spectrum, Ergodic Theory Dynam. Systems 25 (2005), 1775-1797.
    • (2005) Ergodic Theory Dynam. Systems , vol.25 , pp. 1775-1797
    • Dinh Cong, N.1
  • 11
    • 73149091411 scopus 로고    scopus 로고
    • On the spectrum of the one-dimensional Schrödinger operator
    • N. Dinh Cong and R. Fabbri, On the spectrum of the one-dimensional Schrödinger operator, Discrete Contin. Dyn. Syst. Ser. B 9 (2008), 541-554.
    • (2008) Discrete Contin. Dyn. Syst. Ser. B , vol.9 , pp. 541-554
    • Dinh Cong, N.1    Fabbri, R.2
  • 12
    • 0010119436 scopus 로고
    • Topological dynamics and linear differential systems
    • R. Ellis and R. A. Johnson, Topological dynamics and linear differential systems, J. Differential Equations 44 (1982), 21-39.
    • (1982) J. Differential Equations , vol.44 , pp. 21-39
    • Ellis, R.1    Johnson, R.A.2
  • 13
    • 0041937762 scopus 로고    scopus 로고
    • Genericity of exponential dichotomy for two-dimensional differential systems
    • R. Fabbri and R. Johnson, Genericity of exponential dichotomy for two-dimensional differential systems, Ann. Mat. Pura Appl. (4) 178 (2000), 175-193.
    • (2000) Ann. Mat. Pura Appl. (4) , vol.178 , pp. 175-193
    • Fabbri, R.1    Johnson, R.2
  • 14
    • 0041937763 scopus 로고    scopus 로고
    • On the nature of the spectrum of the quasi-periodic Schrödinger operator
    • R. Fabbri, R. Johnson, and R. Pavani, On the nature of the spectrum of the quasi-periodic Schrödinger operator, Nonlinear Anal. Real World Appl. 3 (2002), 37-59.
    • (2002) Nonlinear Anal. Real World Appl. , vol.3 , pp. 37-59
    • Fabbri, R.1    Johnson, R.2    Pavani, R.3
  • 15
    • 0031521310 scopus 로고    scopus 로고
    • On the multiplicative ergodic theorem for uniquely ergodic systems
    • A. Furman, On the multiplicative ergodic theorem for uniquely ergodic systems, Ann. Inst. H. Poincaré Probab. Statist. 33 (1997), 797-815.
    • (1997) Ann. Inst. H. Poincaré Probab. Statist. , vol.33 , pp. 797-815
    • Furman, A.1
  • 17
    • 51249181642 scopus 로고
    • Une méthode pour minorer les exposants de Lyapounov et quelques exemples montrant le caractère local d'un théorème d'Arnol'd et de Moser sur le tore de dimension 2
    • M.-R. Herman, Une méthode pour minorer les exposants de Lyapounov et quelques exemples montrant le caractère local d'un théorème d'Arnol'd et de Moser sur le tore de dimension 2, Comment. Math. Helv. 58 (1983), 453-502.
    • (1983) Comment. Math. Helv. , vol.58 , pp. 453-502
    • Herman, M.-R.1
  • 18
    • 0037534540 scopus 로고
    • Exponential dichotomy, rotation number, and linear differential operators with bounded coefficients
    • R. A. Johnson, Exponential dichotomy, rotation number, and linear differential operators with bounded coefficients, J. Differential Equations 61 (1986), 54-78.
    • (1986) J. Differential Equations , vol.61 , pp. 54-78
    • Johnson, R.A.1
  • 19
    • 37849048093 scopus 로고    scopus 로고
    • Density of hyperbolicity in dimension one
    • O. Kozlovski, W. Shen, and S. Van Strien, Density of hyperbolicity in dimension one, Ann. of Math. (2) 166 (2007), 145-182.
    • (2007) Ann. of Math. , vol.166 , Issue.2 , pp. 145-182
    • Kozlovski, O.1    Shen, W.2    Van Strien, S.3
  • 20
    • 0036014157 scopus 로고    scopus 로고
    • Singular spectrum of Lebesgue measure zero for one-dimensional quasicrystals
    • D. Lenz, Singular spectrum of Lebesgue measure zero for one-dimensional quasicrystals, Comm. Math. Phys. 227 (2002), 119-130.
    • (2002) Comm. Math. Phys. , vol.227 , pp. 119-130
    • Lenz, D.1
  • 21
    • 0003535075 scopus 로고
    • Interscience Tracts in Pure and Applied Mathematics 12, Interscience, New York
    • W. Rudin, Fourier Analysis on Groups, Interscience Tracts in Pure and Applied Mathematics 12, Interscience, New York, 1962.
    • (1962) Fourier Analysis on Groups
    • Rudin, W.1
  • 22
    • 21444433761 scopus 로고    scopus 로고
    • Bounded eigenfunctions and absolutely continuous spectra for one-dimensional Schrödinger operators
    • B. Simon, Bounded eigenfunctions and absolutely continuous spectra for one-dimensional Schrödinger operators, Proc. Amer. Math. Soc. 124 (1996), 3361-3369.
    • (1996) Proc. Amer. Math. Soc. , vol.124 , pp. 3361-3369
    • Simon, B.1
  • 23
    • 33750537342 scopus 로고    scopus 로고
    • Some questions and remarks about SL(2,R{double-struck}) cocycles
    • Cambridge Univ. Press, Cambridge
    • J.-C. Yoccoz, "Some questions and remarks about SL(2,R{double-struck}) cocycles" in Modern Dynamical Systems and Applications, Cambridge Univ. Press, Cambridge, 2004, 447-458.
    • (2004) Modern Dynamical Systems and Applications , pp. 447-458
    • Yoccoz, J.-C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.