Wednesday, August 9

MS1
Applications of Invariant Manifold Theory

1:30 PM-3:30 PM
Koali (Salon 5)

Invariant manifolds and foliations are fundamental geometric structures in studying dynamical systems generated by ODEs and PDEs. They provide coordinates in which the systems can be partially decoupled and normal forms can be derived. Combined with other tools, they are very useful in tracking qualitative behaviors in neighborhoods of invariant sets. In this minisymposium, the speakers will discuss applications in nonlinear optics modeled by the Maxwell-Bloch PDE, time-dependent parabolic PDEs, geometric singular perturbation problems with turning points, and construction of homoclinic orbits for a diffusive near integrable NLS.

1:30-1:55 Invariant Bundles and Principle Spectrum for Certain Time-Dependent Parabolic Operators

V. Hutson, The University of Sheffield, United Kingdom; Wenxian Shen, Auburn University, USA; and G. T. Vickers, The University of Sheffield, United Kingdom

2:00-2:25 Turbulent Dynamics of Long Ring Lasers

Gregor Kovacic, Rensselaer Polytechnic Institute, USA; Victor Royburd, Rensselaer Polytechnic Institute, USA; Ilya Timofeyev and Chongchun Zeng, Courant Institute of Mathematical Sciences, New York University, USA ����

2:30-2:55 Invariant Manifolds for Singular Perturbations with Turning Points

Weishi Liu, University of Kansas, USA

3:00-3:25 Homoclinic Orbits for Singularly Perturbed NLS

Chongchun Zeng, Organizer