WCNA'2008

Qualitative Theory and Applications of Dynamical Systems

session survey

(USA, Orlando, July, 2008)

F.Botelho

The University of Memphis

Department of Mathematical Sciences

373 Dunn Hall, Memphis, Tennessee 38152-3420, USA

V.A.Gaiko

Department of Mathematics

Belarusian State University of Informatics and Radioelectronics

L.Beda Str. 6-4, Minsk 220040, Belarus

1. Introduction

In this paper, we summarize the topics presented at the Fifth World Congress of Nonlinear Analysts in the special session entitled "Qualitative Theory and Applications of Dynamical Systems" and organized by F.Botelho and V.A.Gaiko. The emphasis of the session was two-folded:

-         qualitative aspects of dynamical systems (from dynamics of planar systems to nonlinear operator differential equations on Hilbert spaces);

-         applications of nonlinear analysis to physical phenomena (such as neural network models of unsupervised learning, synchronization aspects of Huygens's pendulum clocks, problems related to elasto-plastic oscillators, and visco-elastic fluids).

The eight invited speakers presented a broad spectrum of mathematical topics including surveys of recent developments and new trends in nonlinear analysis. Most presentations shared a core of underlying techniques from the classical theory of differential, partial differential equations, as well as smooth dynamical systems.

1.             F.Botelho, J.Jamison (University of Memphis, Memphis, USA). ODE in Hilbert spaces motivated by learning models.

2.             T.Hagen (University of Memphis, Memphis, USA) Asymptotics of viscoelastic wedge flow.

3.             J.Tolosa (Stockton College, New Jersey, USA). Geometric methods for the study of local stability.

4.             R.Dilão (Instituto Superior Técnico, Lisboa, Portugal). Synchronizing Huygens's pendulum clocks.

5.             D.Bambusi (University of Milan, Milan, Italy), D.Muraro (Instituto Superior Técnico, Lisboa, Portugal), T.Penati (University of Milan, Milan, Italy). Boundary and dimensional effects on metastability in lattices of weakly coupled oscillators.

6.             J.Turi (University of Texas in Dallas, USA). Degenerate Dirichlet problems related to the invariant measure of elasto-plastic oscillators.

7.             J.Giné (Universitat de Lleida, Lleida, Spain). On the center problem for planar polynomial differential systems.

8.             S.Lynch (Manchester Metropolitan University, Manchester, UK). Neuronal computing.