## YINGFEI YI

School of Mathematics
Georgia Institute of Technology
Atlanta, GA 30332-0160
Phone: (404) 894-4568
Fax: (404) 894-4409
Email: yi@math.gatech.edu
Office: Skiles 237B

# PUBLICATIONS AND PREPRINTS

### Stochastic Dynamics/Fokker-Planck Equations

Integral identity and measure estimates for stationary Fokker-Planck equations (with W. Huang, M. Ji, and Z. Liu), Ann. Probab., to appear.

Steady states of Fokker-Planck equations: I. Existence (with W. Huang, M. Ji, and Z. Liu), submitted

Steady states of Fokker-Planck equations: III. Degenerate diffusion (with W. Huang, M. Ji, and Z. Liu), submitted

Bifurcations in a stochastic business cycle model (with D.-W. Huang and H. Wang), Int. J. Bifur. Chaos Appl. Sci. Engrg., Vol 20 No. 12 (2010), 4111-4118

### Hamiltonian Systems/KAM Theory

Viscous stability of Lagrangian tori (with Z. Liang and J. Yan), Ergod. Th. & Dynam. Sys., Vol 34 (2014), 185-210

Littlewood problem for a singular subquadratic potential (with X. Li), Fields Inst. Commun., Vol 64 (2013), 193-209

Invariant tori for Hamiltonian systems with high order proper degeneracy (with Y. Han and Y. Li), Ann. Henri Poincar\'e, Vol 8 No 10} (2010), 1419-1436

Quasi-periodic breathers in Hamiltonian networks of long-range coupling (with J. Geng and J. Viveros), Physica D, Vol 237 (2008), 2866-2892

A KAM theorem for Hamiltonian networks with long ranged couplings (with J. Geng), Nonlinearity, Vol 20 No 6 (2007), 1313-1342

Quasiperiodic dynamics in Bose-Einstein condensates in periodic lattices and superlattices (with M. van Noort, M. A. Porter, and S.-N. Chow), J. Nonl. Sci., Vol 17 No 1 (2007), 59-83

Quasi-periodic solutions in a nonlinear Schr\"odinger equation (with J. Geng), J. Differential Equations, Vol 233 No 2 (2007), 512-542

Nekhoroshev and KAM stabilities in generalized Hamiltonian systems (with Y. Li), J. Dyn. Diff. Equat., Vol 18 No 3 (2006), 577-614

On exact Poisson structures (with X. Zhang), Fields Inst. Commun., Vol 48 (2006), 291-311

Degenerate lower dimensional tori in Hamiltonian systems (with Y. Han and Y. Li), J. Differential Equations, Vol 227 (2006), 670-691

Persistence of lower dimensional tori of general types in Hamiltonian systems (with Y. Li), Trans. Amer. Math. Soc., Vol 357 (2005), 1565-1600

Persistence of hyperbolic tori in Hamiltonian systems (with Y. Li), J. Differential Equations, Vol 208 (2005), 344-387

Quasiperiodic dynamics in Hamiltonian $1{1\over 2}$ degree of freedom systems away from integrability (with S.-N. Chow and M. van Noort), J. Differential Equations, Vol 212 (2005), 366-393

On Poincar\'e - Treshchev tori in Hamiltonian systems (with Y. Li), Proc. Equadiff2003, Dumortier et al (Ed.), World Scientific, 2005, 136-151

A quasi-periodic Poincare's Theorem (with Y. Li), Math. Annalen, Vol 326 (2003), 649-690

Persistence of invariant tori on submanifolds in Hamiltonian systems (with S-N. Chow and Y. Li), J. Nonl. Sci., Vol 12, No 6 (2002), 585-617

Persistence of invariant tori in generalized Hamiltonian systems (with Y. Li), Ergod. Th. & Dynam. Sys., Vol 22 (2002), 1233-1261

### Topological Dynamics/Ergodic Theory

Dimension of stable sets and scrambled sets (with C. Fang, W. Huang, and P. Zhang), Ergod. Th. & Dynam. Sys., Vol 32 No 2 (2012), 599-628

On Lyapunov exponents of continuous Schr\"{o}dinger cocycles over irrational rotation (with W. Huang), Proc. Amer. Math. Soc., Vol 140 No 9 (2012), 1957-1962

Entropy of dynamical systems with repetition property (with W. Huang and L. Xu), J. Dyn. Diff. Equat. Vol 23 (2011), 683-693

Almost periodically forced circle flows (with W. Huang), J. Fuct. Anal., Vol 257 No 3 (2009), 832-902

A local variational principle of pressures and its applications to equilibrium states (with W. Huang), Israel J. Math., Vol 161 (2007), 29-74

On almost automorphic oscillations, Fields Inst. Commun., Vol 42 (2004), 75-99

On almost automorphic dynamics in symbolic lattices (with A. Berger and S. Siegmund), Ergod. Th. & Dynam. Sys., Vol 24 No 3 (2004), 677-696

Almost automorphic and almost periodic dynamics in skew-product semiflows, Part I: Almost automorphy and almost periodicity; Part II (with W. Shen): Skew-product semiflows; Part III (with W. Shen): Applications to differential equations, Memoirs Amer. Math. Soc., Vol 136 No 647 (1998), 1-93

Topological dynamics and differential equations (with G. R. Sell and W. Shen), Contemp. Math., Vol 215 (1997), 279-297

Ergodicity of minimal sets in scalar parabolic equations (with W. Shen), J. Dyn. Diff. Equat., Vol 8 No 2 (1996), 299-323

On minimal sets of scalar parabolic equations with skew-product structure (with W. Shen), Trans. Amer. Math. Soc., Vol 347 No 11 (1995), 4413-4431

Dynamics of almost periodic scalar parabolic equations (with W. Shen), J. Differential Equations, Vol 122 No 1 (1995), 114-136

Asymptotic almost periodicity of scalar parabolic equations with almost periodic time dependence (with W. Shen), J. Differential Equations, Vol 122 No 2 (1995), 373-397

### Singular Perturbation/Math Biology

Poisson-Nernst-Planck systems for ion flow with a local hard-sphere potential for ion sizes effects (with G. Lin, W. Liu, and M. Zhang), SIAM J. Appl. Dyn. Sys., Vol 12 No 3 (2013), 1613-1648

Quantification of degeneracy in biological systems for characterization of functional interactions between modules (with Y. Li, G. Dwivedi, W. Huang, and M. Kemp), J. Theoret. Biol., Vol 302 (2012), 29-38

Nonlinear oscillations and multiscale dynamics in a closed chemical reaction system (with Y.-F. Li and H. Qian), J. Dyn. Diff. Equat., Vol 22 No 3 (2010), 491-507

Oscillation and multiscale dynamics in a closed chemical reaction system: Second law of thermodynamics and temporal complexity (with Y.-F. Li and H. Qian), J. Chem. Phys. Vol. 129 No. 15 (2008), 154505

Spreading speeds and travelling waves for periodic evolution systems (with X. Liang and X. Zhao), J. Differential Equations, Vol 231 No 1 (2006), 57-77

Malaria epidemics and the sickle-cell gene dynamics (with Z. Feng and H. Zhu), J. Dyn. Diff. Equat., Vol 16 No 4 (2004), 869-896

A metapopulation model with explicit local population dynamics (with Z. Feng, R. Swihart and H. Zhu), J. Math. Biosci. Eng., Vol 1 No 1 (2004) 131-145

Relaxation oscillations in a class of predator-prey systems (with W. Liu and D. Xiao), J. Differential Equations, Vol 188 (2003), 306-331

Travelling wave solutions in a tissue interaction model (with S. Ai and S.-N. Chow), J. Dyn. Diff. Equat., Vol 15 No 2/3 (2003), 517-534

Metapopulation dynamics with migration and local competition (with Z. Feng and H. Zhu), Fields Inst. Commun., Vol 36 (2003), 119-133

Convergence in almost periodic Fisher and Kolmogorov models (with W. Shen), J. Math. Bio., Vol 37 (1998), 84-102

### Bifurcation/Invariant Manifolds

Planar analytic nilpotent germs via analytic first integrals (with X. Zhang), preprint

First integrals and normal forms for germs of analytic vector fields (with J. Chen and X. Zhang), J. Differential Equations, Vol 245 (2008), 1167-1184

The cyclicity of period annulus of degenerate quadratic Hamiltonian system with elliptic segment (with S.-N. Chow and C. Li), Ergod. Th. & Dynam. Sys., Vol 22 (2002), 349-374

Center manifolds for invariant sets of flows (with S.-N. Chow and W. Liu), J. Differential Equations, Vol 168 No 2 (2000), 355-385

Center manifolds of invariant manifolds (with S.-N. Chow and W. Liu), Trans. Amer. Math. Soc., Vol 352 No 11 (2000), 5179-5211

Center manifolds and stability for skew-product flows (with S.-N. Chow), J. Dyn. Diff. Equat., Vol 6 No 4 (1994), 543-582

Hopf bifurcation from non-periodic solutions of differential equations II (with R. A. Johnson), J. Differential Equations, Vol 107 No 2 (1994), 310-340

Generalized integral manifold theorem, J. Differential Equations, Vol 102 No 1 (1993), 153-187

Stability of integral manifold and orbital attraction of quasi-periodic motion, J. Differential Equations, Vol 102 No 2 (1993), 278-322

### Elliptic Equations/Variational Method

A variational problem related to phase transition of liquid crystals (with X. Pan), Commun. Appl. Nonl. Anal., Vol 5 No 1 (1998), 1-31

The Melnikov method and elliptic equations with critical exponent (with R. A. Johnson and X. Pan), Indiana Univ. Math. J., Vol 43 No 3 (1994), 1045-1077

Singular solutions of elliptic equation $\Delta u - u + u^p = 0$ (with R. A. Johnson and X. Pan), Annali di Matematic\'a prera ed Appli\'cata (IV), Vol CLXVI (1994), 203-225

Positive solutions of super-critical elliptic equations and asymptotics (with R. A. Johnson and X. Pan), Commun. Partial Diff. Equat., Vol 18 (5&6) (1993), 977-1019

Singular ground states of semi-linear elliptic equations via invariant manifolds theory (with R. A. Johnson and X. Pan), Nonlear Anal., TMA, Vol 20 (1993), 1279-1302