Saturday, August 12

Conley Index and Related Topological Methods

1:30 PM-3:30 PM
Hibiscus & Ulima (Salon 3 & 4)

In this minisymposium, the speakers will present recent developments in the Conley index theory and other related topological methods. Topological methods are particularly useful in studying dynamical systems when one has only crude information about the systems of interest. The speakers will discuss singularly perturbed ODEs called slow-fast systems from Conley index point of view, detection of homoclinic/heteroclinic tangencies of maps using discrete Conley index theory, and stability of some specific solutions in PDEs as examples of the power of topological methods in applications as well as their new theoretical ideas.

Organizer: Hiroe Oka
Ryukoku University, Japan
1:30-1:55 A Conley Index for Random Dynamical Systems
Konstantin Mischaikow, Georgia Institute of Technology, USA
2:00-2:25 Chaotic Solutions in Slowly Varying Perturbations of Hamiltonian Systems with Applications to Shallow Water Sloshingi
Tomâs Gedeon, Montana State University, USA; Hiroshi Kokubu, Kyoto University, Japan; Konstantin Mischaikow, Georgia Institute of Technology, USA; and Hiroe Oka, Organizer
2:30-2:55 A Topological Method for the Stability Problem of Traveling Waves
Shunsaku Nii, Saitama University, Japan
3:00-3:25 Homoclinic Bifurcations and the Conley Index
Zin Arai, Kyoto University, Japan

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