Jiangong You

Cheung Kong Scholar Professor
Professor of Mathematics
Chair of Department of Mathematics
Nanjing University

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Contact information:

Office: Room 1101, Mengminwei Building

Tel: +086-025-83686437

Email: jyou@nju.edu.cn

Mailing address: Department of Mathematics, Nanjing University, Hankou Road 22nd, Nanjing, Jiangsu, China, 210093

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Research Interests:

Differential Equations, Dynamical Systems, Dynamics of Hamiltonian PDEs, Spectral Theory of Schrödinger Operators

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Preprints:

• Point Spectrum of the Quasi-Periodic Long Range Operators. Preprint.
  J. You, S. Zhang and Q. Zhou.
• Phase Transition and Semi-Global Reducibility. Preprint.
  J. You and Q. Zhou.

Accepted for publication:

• Localization in One-dimensional Quasi-periodic Nonlinear Systems. To appear in Geometric And Functional Analysis. Preprint.
  J. Geng, J. You and Z. Zhao.
• Examples of Discontinuity of Lyapunov Exponent in Smooth Quasi-Periodic Cocycles. To appear in Duke Mathematical Journal 2013. Preprint.
  Y. Wang and J. You
• Embedding of Analytic Quasi-Periodic Cocycles into Analytic Quasi-Periodic Linear Systems and its Applications. To appear in Communications in Mathematical Physics 2013. Preprint.
  J. You and Q. Zhou
• Reducibility of Slow Quasi-Periodic Linear Systems. To appear in Proceedings of the American Mathematical Society 2013. Preprint.
  J. Wu and J. You
• Hölder continuity of the Lyapunov exponent for analytic quasiperiodic Schrödinger cocycle with weak Liouville frequency. To appear in Ergod. Th. & Dynam. Sys. 2013. Preprint.
  J. You and S. Zhang

Publications:

Note: The button marked Article provides a pdf of the article for your personal, non-commercial use and should not be reposted. E-Journal will take you to the journal site and require you or your institution to have a subscription.

• Almost reducibility and non-perturbative reducibility of quasi-periodic linear systems.  Invent. Math. 190 (2012), no. 1, 209–260. Article; E-Journal.
  X. Hou and J. You
• An infinite dimensional KAM theorem and its application to the two dimensional cubic Schrödinger equation.  Adv. Math. 226 (2011), no. 6, 5361–5402.  Article; E-Journal.
  J. Geng, X. Xu and J. You
• Persistence of the non-twist torus in nearly integrable Hamiltonian systems. Proc. Amer. Math. Soc. 138 (2010), no. 7, 2385–2395. Article; E-Journal.
  J. Xu and J. You
• Local rigidity of reducibility of analytic quasi-periodic cocycles on U(n). Discrete Contin. Dyn. Syst. 24 (2009), no. 2, 441–454. Article; E-Journal.
  X. Hou and J. You
• Corrigendum for the paper: "Two-dimensional invariant tori in the neighborhood of an elliptic equilibrium of Hamiltonian systems" in Acta Mathematica Sinica, English Series August 2009, Volume 25, Issue 8, pp 1363-1378. Article
  H. Lu and J. You
• Two-dimensional invariant tori in the neighborhood of an elliptic equilibrium of Hamiltonian systems.  Acta Mathematica Sinica, English Series August 2009, Volume 25, Issue 8, pp 1363-1378. Article; E-Journal.
  H. Lu and J. You
• Full measure reducibility for generic one-parameter family of quasi-periodic linear systems. J. Dynam. Differential Equations 20 (2008), no. 4, 831–866. Article; E-Journal.
  H. He and J. You
• The rigidity of reducibility of cocycles on  SO(N ,R). Nonlinearity 21 (2008),no. 10, 2317–2330. Article; E-Journal.
  X. Hou and J. You
• Diophantine vectors in analytic submanifolds of Euclidean spaces. Sci. China Ser. A. 50 (2007), no. 9, 1334–1338. Article; E-Journal.
  R. Cao and J. You
• Corrigendum for the paper: "Invariant tori for nearly integrable Hamiltonian systems with degeneracy" [Math. Z. 226 (1997), no. 3, 375–387] by Xu, You, and Q. Qiu. Math. Z. 257 (2007), no. 4, 939. Article; E-Journal.
  J. Xu and J. You
• Gevrey-smoothness of invariant tori for analytic nearly integrable Hamiltonian systems under Rüssmann's non-degeneracy condition. J. Differential Equations 235 (2007), no. 2, 609–622. Article; E-Journal.
  J. Xu and J. You
• KAM Tori for Higher Dimensional Beam Equation with Constant Potentials, Nonlinearity 19 (2006), no. 10, 2405–2423. Article; E-Journal.
  J. Geng and J. You
• The Existence of Integrable Invariant Manifolds of Hamiltonian Partial Differential Equations, Discrete and Continuous Dynamical Systems 16 (2006), no. 1, 227–234. Article; E-Journal.
  R.Cao and J. You
• An Improved Result for Positive Measure Reducibility of Quasi- periodic Linear Systems, Acta Mathematica Sinica (English series) 22 (1), 2006, 77-86. Article; E-Journal.
  H. He and J. You
• A KAM Theorem for Partial Differential Equations in Higher Dimensional Space, Communications in Mathematical Physics, Vol.262(2), 2006, 343-372. Article; E-Journal.
  J.Geng and J.You
• Umbilical Torus Bifurcations in Hamiltonian Systems,  J. Differential Equations, Vol. 222(1), 2006, 233-262. Article; E-Journal.
  H. Broer, H. Hanssmann and J. You
• A simple proof of diffusion approximations for LBFS re-entrant lines, Oper. Res. Lett., 34(2006), no. 2, 199–204. Article; E-Journal.
  J. Yang, J.G. Dai, J. You and H. Zhang
• Quasi-Periodic Solutions for 1D Schrödinger Equations with Higher Order Nonlinearity, SIAM J. Mathematical Analysis, 36(2005), 1965-1990. Article; E-Journal.
  Z. Liang and J. You
• Bifurcations of Normally Parabolic Tori in Hamiltonian Systems, Nonlinearity, 18 (2005) 1735-1769. Article; E-Journal.
  H. Broer, H. Hanssmann and J. You
• A KAM Theorem for One Dimensional Schrödinger Equation with Periodic Boundary Conditions, J. Differential Equations, 209, 2005, 1-56. Article; E-Journal.
  J. Geng and J. You
• KAM tori of Hamiltonian perturbations of 1D linear beam equations, J.Math.Anal.Appl., 277, 2003, 104-121. Article; E-Journal.
  J. Geng and J. You
• A Symplectic Map and its Application to the Persistence of Lower Dimensional InvariantTori, Science in China, 45(5), 2002,598-603. Article; E-Journal.
  J. Xu and J. You
• Persistence of lower dimensional tori under the first Melnikov’s non-resonance condition, Journal de Mathematiques Pures et Appliquees, 80 (10), 2001, 1045-1067. Article; E-Journal.
  J. Xu and J. You
• KAM theory for lower dimensional tori of nearly integrable Hamiltonian systems, Progress in Nonlinear Analysis, edited by K-C.Chang and Y. Long, World Scientific, 2000, 409-423. Article; E-Journal.
  J. You
• KAM tori for 1D nonlinear wave equations with periodic boundary conditions, Communications in Mathematical Physics, Vol.211(2), 497-525, 2000. Article; E-Journal.
  L. Chierchia and J. You
• KAM-type theorem on resonant surfaces for nearly integrable Hamiltonian systems, J. Nonlinear Science, Vol.10, 49-68, 2000. Article; E-Journal.
  F-Z. Cong, T. Kupper, Y. Li and J. You
• Lower dimensional tori of reversible Hamiltonian systems in the resonant zone, Dynamical Systems, Proceedings of the International Conference in Honor of Professor Liao Shantao, 9-12, August,1998. Editors, Yunping Jiang, Lan Wen, World Scientific, 1999, 301-314.
  J. You
• Perturbations of lower dimensional tori for Hamiltonian systems, J.Differential Equations, Vol. 152, 1-29, 1999. Article; E-Journal.
  J. You
• Existence of quasiperiodic solutions and Littlewood's boundedness problem of Duffing equations with subquadratic potentials, Nonlinear Anal. 35 (1999), no. 5, Ser. A: Theory Methods,549-559. Article; E-Journal.
  T. Kupper and J. You
• A KAM theorem for hyperbolic type degenerate lower dimensional tori in Hamiltonian systems, Communications in Mathematical Physics, Vol.192, 145-168, 1998. Article; E-Journal.
  J. You
• Quasiperiodic solutions of Duffing's Equations, J. Nonlinear Analysis: TMA, 1998. Article; E-Journal.
  B. Liu and J. You
• Oscillatory escape in a Duffing equation with Polynomial potentials, J. Differential Equations, Vol.140, pp 415-426, 1997. Article; E-Journal.
  M. Levi and J. You
• On the Application of KAM Theory to Discontinuous Dynamical Systems, J. Differential Equations, Vol. 139, pp.1-21, 1997. Article; E-Journal.
  M. Kunze, T. Kupper and J. You
• Invariant tori of nearly integrable Hamiltonian systems with degeneracy, Mathematische Zeitschrift, Vol.226, 375-386, 1997. Article; E-Journal.
  J. Xu, Q. Qiu and J. You
• A KAM Theorem of Degenerate Infinite Dimensional Hamiltonian Systems(I，II), Science in China, Vol.39(4), 372-394, 1996. Article; E-Journal.
  J. Xu, Q. Qiu and J. You
• Boundedness of solutions for time dependent polynomial potentials with C2 coefficients, Z. Angew. Math. Phys. , Vol. 47, 1996. Article; E-Journal.
  Y. Wang and J. You
• On reducibility of linear differential equations with almost periodic coefficients, Chinese Journal of Contemporary Mathematics, Vol.17 (1996), 375-386.
  J. Xu and J. You
• Quasiperiodic solutions for a class of quasiperiodic forced differential equations, J. Math. Anal. and Appl. Vol.192(3),1995. Article; E-Journal.
  J. You
• Stability of a parabolic fixed point of reversible mappings, Chin. Ann. of Math. (Series B), Vol. 15(2), 1994, 147-152.
  B. Liu and J. You
• Quasiperiodic solutions for nonlinear differential equations of second order with symmetry. A Chinese summary appears in Acta Math. Sinica 38 (1995), no. 4, 574. Acta Math. Sinica (N.S.) 10 (1994),no. 3, 231–242. Article; E-Journal.
  B. Liu and J. You
• Periodic solutions of forced second order equations with the oscillatory time map, Differential and Integral Equations，Vol. 6(4) 793-806, 1993.
  D. Qian and J.You
• Boundedness for solutions of superlinear Duffing's equations via the twist theorem, Science in China(series A), 35(4), 1992, 399-412.
  J. You
• Boundenness of solutions and quasiperiodic solutions of nonconservative pendulum systems in a certain class, Chinese Bulletin of Science (Kexue Tongbao), 36(21),1991, 1906-1909.
  J. You
• Invariant tori and Lagrange stability of pendulum type equations, J. Diffential Equations, 85(1), 1990, 54-65. Article; E-Journal.
  J. You

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Teaching:

• Mathematical Analysis (Fall 2005-2008, undergraduate freshman courses).
• Geometrical Methods in the Theory of Ordinary Differential Equations (Fall 2009-2011, undergraduate junior courses).
• Seminar of Dynamical Systems (Spring 2011-2013, undergraduate junior courses).
• Dynamical Systems (Spring 2008-2010, graduate courses).
• Differential Dynamical Systems (Spring 2011, graduate course).
• Hamiltonian Systems and N-Body Problems(Spring 2012, graduate course).
• Chaos in Dynamical Systems (Spring 2013, graduate course).

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Links:

• List of J.You's papers from the AMS MathSciNet with links to Mathematical Reviews. (Click here).
• arXiv.org, my preprint.
• print.google.com.
• scholar.google.com.
• Math Department of NJU .

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