Yingfei Yi, Ph.D

Killam Memorial Chair, Faculty of Science - Mathematics & Statistical Sciences

Contact

Killam Memorial Chair, Faculty of Science - Mathematics & Statistical Sciences
Email
yingfei@ualberta.ca
Phone
(780) 492-0215
Address
501 Central Academic Building
11324 - 89 Ave NW
Edmonton AB
T6G 2G1

Overview

Research

My research focuses on Dynamical Systems and Differential Equations, concerning both theoretical developments and applications. Areas I have been working on include Stochastic Differential Equations, Fokker-Planck Equations, Hamiltonian Systems, KAM Theory, Topological Dynamics, Ergodic Theory, Non-automatics Systems, Skew-Product Flows, Singular Perturbations, Mathematical Biology, Bifurcations, Invariant Manifolds Theory, Elliptic Equations, Parabolic Equations, Solitary Equations, and Variational Method. Publication


Announcements

Courses

MATH 432 - Intermediate Differential Equations

Elementary existence and uniqueness theorems. Systems of equations, stability, perturbation theory. Introduction to numerical methods. Introduction to phase plane analysis. Prerequisite: One of MATH 201, 334 or 336.

Fall Term 2020
MATH 524 - Ordinary Differential Equations IIA

Existence theorems, uniqueness theorems; linear systems (basic theory); stability (basic theory); nonlinear systems (local theory); nonlinear systems (global theory); bifurcations. Prerequisite: MATH 334 or 336, or equivalent.

Fall Term 2020

Scholarly Activities

Publications

Systematic measures of biological networks, Part II: Degeneracy, complexity and robustness
Author(s): Y. Li and Y. Yi
Publication Date: 2016
Publication: Comm. Pure Appl. Math.
Volume: To appear

Turing points and relaxation oscillation cycles in simple epidemic models
Author(s): M. Li, W. Liu, C. Shan, and Y. Yi
Publication Date: 2016
Publication: SIAM J. Appl. Math.
Volume: 76
Issue: 2
Page Numbers: 663-687

Interior regularity for regional fractional Laplacian
Author(s): C. Mou and Y. Yi
Publication Date: 2015
Publication: Comm. Math. Phys.
Volume: 340
Page Numbers: 233-251

Integral identity and measure estimates for stationary Fokker-Planck equations
Author(s): W. Huang, M. Ji, Z. Liu, and Y. Yi
Publication Date: 2015
Publication: Ann. Probab.
Volume: 43
Issue: 4
Page Numbers: 1712-1730

Viscous stability of quasi-periodic tori
Author(s): Z. Liang, J. Yan, and Y. Yi
Publication Date: 2014
Publication: Ergod. Th. Dynam. Sys.
Volume: 34
Page Numbers: 185-210

Invariant tori for Hamiltonian systems with high order proper degeneracy
Author(s): Y. Han, Y. Li, Y. Li
Publication Date: 2010
Publication: Ann. Henri Poincare
Volume: 10
Issue: 8
Page Numbers: 1419-1436

Almost periodically forced circle flow
Author(s): W. Huang and Y. Yi
Publication Date: 2009
Publication: J. Funct. Anal.
Volume: 257
Issue: 3
Page Numbers: 832-902

Quasi-periodic breathers in Hamiltonian networks of long-range coupling
Author(s): J. Geng, J. Viveros, and Y. Yi
Publication Date: 2008
Publication: Physica D
Volume: 237
Page Numbers: 2866-2892

A local variational principle of pressure and its applications to equilibrium states
Author(s): W. Huang and Y. Yi
Publication Date: 2007
Publication: Israel J. Math.
Volume: 161
Page Numbers: 29-74

Persistence of lower dimensional tori of general types in Hamiltonian systems
Author(s): Y. Li and Y. Li
Publication Date: 2005
Publication: Trans. Amer. Math. Soc.
Volume: 357
Page Numbers: 1565-1600

A quasi-periodic Poincare's theorem
Author(s): Y. Li and Y. Li
Publication Date: 2003
Publication: Math. Annalen
Volume: 326
Page Numbers: 649-690

The cyclicity of period annulus of degenerate quadratic Hamiltonian system with elliptic seg- ment
Author(s): S.-N. Chow, C. Li, and Y. Yi
Publication Date: 2002
Publication: Ergod. Th. Dynam. Sys.
Volume: 22
Page Numbers: 349-374

Center manifolds of invariant manifolds
Author(s): S.-N. Chow, W. Liu, and Y. Yi
Publication Date: 2000
Publication: Trans. Amer. Math. Soc.
Volume: 352
Issue: 11
Page Numbers: 5179-5211

Almost automorphic and almost periodic dynamics in skew-product semi-flows
Author(s): W. Shen and Y. Yi
Publication Date: 1998
Publication: Memoirs Amer. Math. Soc.
Volume: 136
Issue: 647
Page Numbers: 1-93

On minimal sets of scalar parabolic equations with skew-product structure
Author(s): W. Shen and Y. Yi
Publication Date: 1995
Publication: Trans. Amer. Math. Soc.
Volume: 347
Issue: 11
Page Numbers: 4413-4431