Qi Zhou (周麒)-Research

作者:dly(2019-06-26)

1. Reducibility results for quasi-periodic cocycles  with Liouvillean frequency(with J.Wang),  Journal  of  Dynamics and  Differential Equations, Volume 24, Issue 1, pp 61-83, 2012.

2. Simultaneous Linearization for commuting quasi-periodically forced circle diffeomorphisms(with J.Wang), Proceedings of the AMS, Volume 141, Number 2, 625-636,  2013.

3. Embedding of analytic quasi-periodic cocycles into analytic quasi-periodic linear systems and its  applications(with J.You) Communications in  Mathematical  Physics, 323, 975-1005, 2013

4. Phase transition and  semi-global reducibility (with J.You). Communications in  Mathematical  Physics,  Volume 330, Issue 3, 1095-1113, 2014.

5. Point Spectrum For Quasi-periodic Long Range Operators (with J.You and S. Zhang).  Journal of spectral theory. Issue 3, 769-781, 2014.

6. Simple Counter-examples to Kotani-Last Conjecture via reducibility (with J. You). International Mathematics Research Notices. No. 19, 9450-9455, 2015

7. Response Solutions for Quasi-periodically Forced Harmonic Oscillators (with J.Wang, J.You).  Transactions of the  AMS, Volume 369, Number 6, June 2017, Pages 4251-4274

8. Sharp Phase transitions  for the almost Mathieu operator (with A.Avila and J.You).Duke Math J,Volume 166, Number 14 (2017), 2697-2718.

9. Second phase transition line (with A. Avila and S. Jitomirskaya)  Math Ann, Volume 370, Issue 1-2, 271-285, 2018

10. Linearization of  quasi-periodically forced circle flow beyond Brjuno condition(with R.Krikorian, J.Wang, J.You).  Comm. Math. Phys,358 (2018), no. 1, 81-100. 

11. Sharp Holder continuity of the Lyapunov exponent of finitely differentiable quasi-periodic cocycles (with  A. Cai, C.Chavaudret and J.You) Math. Z.291 (2019), no. 3-4, 931-958.

12. Positive Hausdorff dimensional spectrum  for the  critical almost Mathieu operator (with B.Helffer, Q.Liu, Y. Qu). Comm. Math. Phys. 368 (2019), no. 1, 369-382.

13.  Genericity of mode-locking for quasiperiodically forced circle maps (with T.Jager, J. Wang). Adv. Math. 348 (2019), 353-377.

14  Asymptotics of spectral gaps of quasi-periodic Schrodinger operators. (with M. Leguil,J. You, Z. Zhao)

15. Quasi-periodic solutions of NLS with liouvillean frequency(with X.Xu, J.You)  To appear in Analysis & PDE.

16. Absolutely Continuous Spectrum of Multifrequency Quasiperiodic Schrodinger operator(with X.Hou, J.Wang)  Journal of Functional Analysis 279(6):108632

17.  Exponential dynamical localization: Criterion and applications(with L.Ge,J.You) To appear in Ann. Sci. ENS. 

18. 1-d Quantum Harmonic Oscillator with Time Quasi-periodic Quadratic Perturbation: Reducibility and Growth of Sobolev Norms(with Z.Liang,Z. Zhao) J. Math. Pures. Appl (9) 146 (2021)

19. One dimensional quasiperiodic mosaic lattice with exact mobility edges(with Y.Wang et al)  Physical Review Letters 125:196604.

20. Anosov-Katok  constructions for quasi-periodic $SL(2,R)$ cocycles (with N.Karaliolios, X.Xu)

21. Exact mobility edges, $PT$-symmetry breaking and skin effect in one-dimensional non-Hermitian quasicrystals (with Y.Liu et al) Phys. Rev. B 103, 014203,2021

22. Localization transition, spectrum structure and winding numbers for one-dimensional non-Hermitian quasicrystals(with Y.Liu and S.Chen)Phys. Rev. B 104, 024201,2021 (Editor's suggestion)

23 Global rigidity for ultra-differentiable quasiperiodic  cocycles and its spectral applications (with H. Cheng, L.Ge,J.You)

24 Absolutely Continuous Spectrum for CMV Operators With Small Quasi-Periodic Verblunsky Coefficients (with L.Li, D. Damanik) To appear in Tran Amer Math Soc

25. Traveling fronts for Fisher-KPP lattice equations in almost periodic media (with X.Liang, H.Wang and T. Zhou)

26. Exact mobility edges for 1D quasiperiodic models (with Y. Wang, X. Xia, J.You, Z. Zheng)

27. On the abominable properties of the almost Mathieu operator with well approximated frequencies(with A.Avila, Y. Last, M.Shamis)

28.Quantitative almost reducibility and Mobius disjointness for analytic quasiperiodic Schrodinger cocycles(with W. Huang, J.Wang, Z.Wang)

29.Cantor Spectrum for CMV Matrices With Almost Periodic Verblunsky Coefficients(with L.Li, D. Damanik)