Almost Mathieu operator (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Almost Mathieu operator" in English language version.

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12doi.org

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9semanticscholar.org

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7harvard.edu

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6arxiv.org

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2zbmath.org

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1encyclopediaofmath.org

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1uci.edu

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arxiv.org

Avila, A. (2008). "The absolutely continuous spectrum of the almost Mathieu operator". arXiv:0810.2965 [math.DS].
Jitomirskaya, Svetlana Ya. (1999). "Metal-insulator transition for the almost Mathieu operator". Ann. of Math. 150 (3): 1159–1175. arXiv:math/9911265. Bibcode:1999math.....11265J. doi:10.2307/121066. JSTOR 121066. S2CID 10641385.
Last, Y.; Simon, B. (1999). "Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrödinger operators". Invent. Math. 135 (2): 329–367. arXiv:math-ph/9907023. Bibcode:1999InMat.135..329L. doi:10.1007/s002220050288. S2CID 9429122.
Avila, A.; Jitomirskaya, S. (2005). "Solving the Ten Martini Problem". The Ten Martini problem. Lecture Notes in Physics. Vol. 690. pp. 5–16. arXiv:math/0503363. Bibcode:2006LNP...690....5A. doi:10.1007/3-540-34273-7_2. ISBN 978-3-540-31026-6. S2CID 55259301.
Puig, Joaquim (2004). "Cantor spectrum for the almost Mathieu operator". Comm. Math. Phys. 244 (2): 297–309. arXiv:math-ph/0309004. Bibcode:2004CMaPh.244..297P. doi:10.1007/s00220-003-0977-3. S2CID 120589515.
Avila, A.; Krikorian, R. (2006). "Reducibility or non-uniform hyperbolicity for quasiperiodic Schrödinger cocycles". Annals of Mathematics. 164 (3): 911–940. arXiv:math/0306382. doi:10.4007/annals.2006.164.911. S2CID 14625584.

caltech.edu

math.caltech.edu

Jitomirskaya, S.; Simon, B. (1994). "Operators with singular continuous spectrum, III. Almost periodic Schrödinger operators" (PDF). Comm. Math. Phys. 165 (1): 201–205. Bibcode:1994CMaPh.165..201J. CiteSeerX 10.1.1.31.4995. doi:10.1007/bf02099743. S2CID 16267690. Zbl 0830.34074.

doi.org

Jitomirskaya, S. (2021). "On point spectrum of critical almost Mathieu operators" (PDF). Advances in Mathematics. 392: 6. doi:10.1016/j.aim.2021.107997.
Jitomirskaya, Svetlana Ya. (1999). "Metal-insulator transition for the almost Mathieu operator". Ann. of Math. 150 (3): 1159–1175. arXiv:math/9911265. Bibcode:1999math.....11265J. doi:10.2307/121066. JSTOR 121066. S2CID 10641385.
Avron, J.; Simon, B. (1982). "Singular continuous spectrum for a class of almost periodic Jacobi matrices". Bull. Amer. Math. Soc. 6 (1): 81–85. doi:10.1090/s0273-0979-1982-14971-0. Zbl 0491.47014.
Jitomirskaya, S.; Simon, B. (1994). "Operators with singular continuous spectrum, III. Almost periodic Schrödinger operators" (PDF). Comm. Math. Phys. 165 (1): 201–205. Bibcode:1994CMaPh.165..201J. CiteSeerX 10.1.1.31.4995. doi:10.1007/bf02099743. S2CID 16267690. Zbl 0830.34074.
Last, Y.; Simon, B. (1999). "Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrödinger operators". Invent. Math. 135 (2): 329–367. arXiv:math-ph/9907023. Bibcode:1999InMat.135..329L. doi:10.1007/s002220050288. S2CID 9429122.
Bourgain, J.; Jitomirskaya, S. (2002). "Continuity of the Lyapunov exponent for quasiperiodic operators with analytic potential". Journal of Statistical Physics. 108 (5–6): 1203–1218. doi:10.1023/A:1019751801035. S2CID 14062549.
Avila, A.; Jitomirskaya, S. (2005). "Solving the Ten Martini Problem". The Ten Martini problem. Lecture Notes in Physics. Vol. 690. pp. 5–16. arXiv:math/0503363. Bibcode:2006LNP...690....5A. doi:10.1007/3-540-34273-7_2. ISBN 978-3-540-31026-6. S2CID 55259301.
Bellissard, J.; Simon, B. (1982). "Cantor spectrum for the almost Mathieu equation". J. Funct. Anal. 48 (3): 408–419. doi:10.1016/0022-1236(82)90094-5.
Puig, Joaquim (2004). "Cantor spectrum for the almost Mathieu operator". Comm. Math. Phys. 244 (2): 297–309. arXiv:math-ph/0309004. Bibcode:2004CMaPh.244..297P. doi:10.1007/s00220-003-0977-3. S2CID 120589515.
Avila, A.; Krikorian, R. (2006). "Reducibility or non-uniform hyperbolicity for quasiperiodic Schrödinger cocycles". Annals of Mathematics. 164 (3): 911–940. arXiv:math/0306382. doi:10.4007/annals.2006.164.911. S2CID 14625584.
Last, Y. (1993). "A relation between a.c. spectrum of ergodic Jacobi matrices and the spectra of periodic approximants". Comm. Math. Phys. 151 (1): 183–192. Bibcode:1993CMaPh.151..183L. doi:10.1007/BF02096752. S2CID 189834787.
Last, Y. (1994). "Zero measure spectrum for the almost Mathieu operator". Comm. Math. Phys. 164 (2): 421–432. Bibcode:1993CMaPh.151..183L. doi:10.1007/BF02096752. S2CID 189834787.

encyclopediaofmath.org

"Mathieu equation". Encyclopedia of Mathematics. Springer. Retrieved February 9, 2024.

harvard.edu

ui.adsabs.harvard.edu

Jitomirskaya, Svetlana Ya. (1999). "Metal-insulator transition for the almost Mathieu operator". Ann. of Math. 150 (3): 1159–1175. arXiv:math/9911265. Bibcode:1999math.....11265J. doi:10.2307/121066. JSTOR 121066. S2CID 10641385.
Jitomirskaya, S.; Simon, B. (1994). "Operators with singular continuous spectrum, III. Almost periodic Schrödinger operators" (PDF). Comm. Math. Phys. 165 (1): 201–205. Bibcode:1994CMaPh.165..201J. CiteSeerX 10.1.1.31.4995. doi:10.1007/bf02099743. S2CID 16267690. Zbl 0830.34074.
Last, Y.; Simon, B. (1999). "Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrödinger operators". Invent. Math. 135 (2): 329–367. arXiv:math-ph/9907023. Bibcode:1999InMat.135..329L. doi:10.1007/s002220050288. S2CID 9429122.
Avila, A.; Jitomirskaya, S. (2005). "Solving the Ten Martini Problem". The Ten Martini problem. Lecture Notes in Physics. Vol. 690. pp. 5–16. arXiv:math/0503363. Bibcode:2006LNP...690....5A. doi:10.1007/3-540-34273-7_2. ISBN 978-3-540-31026-6. S2CID 55259301.
Puig, Joaquim (2004). "Cantor spectrum for the almost Mathieu operator". Comm. Math. Phys. 244 (2): 297–309. arXiv:math-ph/0309004. Bibcode:2004CMaPh.244..297P. doi:10.1007/s00220-003-0977-3. S2CID 120589515.
Last, Y. (1993). "A relation between a.c. spectrum of ergodic Jacobi matrices and the spectra of periodic approximants". Comm. Math. Phys. 151 (1): 183–192. Bibcode:1993CMaPh.151..183L. doi:10.1007/BF02096752. S2CID 189834787.
Last, Y. (1994). "Zero measure spectrum for the almost Mathieu operator". Comm. Math. Phys. 164 (2): 421–432. Bibcode:1993CMaPh.151..183L. doi:10.1007/BF02096752. S2CID 189834787.

jstor.org

Jitomirskaya, Svetlana Ya. (1999). "Metal-insulator transition for the almost Mathieu operator". Ann. of Math. 150 (3): 1159–1175. arXiv:math/9911265. Bibcode:1999math.....11265J. doi:10.2307/121066. JSTOR 121066. S2CID 10641385.

projecteuclid.org

Last, Y. (1993). "A relation between a.c. spectrum of ergodic Jacobi matrices and the spectra of periodic approximants". Comm. Math. Phys. 151 (1): 183–192. Bibcode:1993CMaPh.151..183L. doi:10.1007/BF02096752. S2CID 189834787.
Last, Y. (1994). "Zero measure spectrum for the almost Mathieu operator". Comm. Math. Phys. 164 (2): 421–432. Bibcode:1993CMaPh.151..183L. doi:10.1007/BF02096752. S2CID 189834787.

psu.edu

citeseerx.ist.psu.edu

Jitomirskaya, S.; Simon, B. (1994). "Operators with singular continuous spectrum, III. Almost periodic Schrödinger operators" (PDF). Comm. Math. Phys. 165 (1): 201–205. Bibcode:1994CMaPh.165..201J. CiteSeerX 10.1.1.31.4995. doi:10.1007/bf02099743. S2CID 16267690. Zbl 0830.34074.

semanticscholar.org

api.semanticscholar.org

Jitomirskaya, Svetlana Ya. (1999). "Metal-insulator transition for the almost Mathieu operator". Ann. of Math. 150 (3): 1159–1175. arXiv:math/9911265. Bibcode:1999math.....11265J. doi:10.2307/121066. JSTOR 121066. S2CID 10641385.
Jitomirskaya, S.; Simon, B. (1994). "Operators with singular continuous spectrum, III. Almost periodic Schrödinger operators" (PDF). Comm. Math. Phys. 165 (1): 201–205. Bibcode:1994CMaPh.165..201J. CiteSeerX 10.1.1.31.4995. doi:10.1007/bf02099743. S2CID 16267690. Zbl 0830.34074.
Last, Y.; Simon, B. (1999). "Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrödinger operators". Invent. Math. 135 (2): 329–367. arXiv:math-ph/9907023. Bibcode:1999InMat.135..329L. doi:10.1007/s002220050288. S2CID 9429122.
Bourgain, J.; Jitomirskaya, S. (2002). "Continuity of the Lyapunov exponent for quasiperiodic operators with analytic potential". Journal of Statistical Physics. 108 (5–6): 1203–1218. doi:10.1023/A:1019751801035. S2CID 14062549.
Avila, A.; Jitomirskaya, S. (2005). "Solving the Ten Martini Problem". The Ten Martini problem. Lecture Notes in Physics. Vol. 690. pp. 5–16. arXiv:math/0503363. Bibcode:2006LNP...690....5A. doi:10.1007/3-540-34273-7_2. ISBN 978-3-540-31026-6. S2CID 55259301.
Puig, Joaquim (2004). "Cantor spectrum for the almost Mathieu operator". Comm. Math. Phys. 244 (2): 297–309. arXiv:math-ph/0309004. Bibcode:2004CMaPh.244..297P. doi:10.1007/s00220-003-0977-3. S2CID 120589515.
Avila, A.; Krikorian, R. (2006). "Reducibility or non-uniform hyperbolicity for quasiperiodic Schrödinger cocycles". Annals of Mathematics. 164 (3): 911–940. arXiv:math/0306382. doi:10.4007/annals.2006.164.911. S2CID 14625584.
Last, Y. (1993). "A relation between a.c. spectrum of ergodic Jacobi matrices and the spectra of periodic approximants". Comm. Math. Phys. 151 (1): 183–192. Bibcode:1993CMaPh.151..183L. doi:10.1007/BF02096752. S2CID 189834787.
Last, Y. (1994). "Zero measure spectrum for the almost Mathieu operator". Comm. Math. Phys. 164 (2): 421–432. Bibcode:1993CMaPh.151..183L. doi:10.1007/BF02096752. S2CID 189834787.

uci.edu

math.uci.edu

Jitomirskaya, S. (2021). "On point spectrum of critical almost Mathieu operators" (PDF). Advances in Mathematics. 392: 6. doi:10.1016/j.aim.2021.107997.

zbmath.org

Avron, J.; Simon, B. (1982). "Singular continuous spectrum for a class of almost periodic Jacobi matrices". Bull. Amer. Math. Soc. 6 (1): 81–85. doi:10.1090/s0273-0979-1982-14971-0. Zbl 0491.47014.
Jitomirskaya, S.; Simon, B. (1994). "Operators with singular continuous spectrum, III. Almost periodic Schrödinger operators" (PDF). Comm. Math. Phys. 165 (1): 201–205. Bibcode:1994CMaPh.165..201J. CiteSeerX 10.1.1.31.4995. doi:10.1007/bf02099743. S2CID 16267690. Zbl 0830.34074.