The three-day event will bring together a number of international experts to report on current advances in the field of Nonlinear Dynamical Systems. The field incorporates the interests of a broad range of studies in the areas of applied mathematics and mathematical physics. In particular, the workshop will focus on dynamical systems exhibiting behavior that lies on the boundary between order and chaos.
Systems exhibiting integrable dynamics appear ubiquitously in natural phenomena. However, even the most simply-defined deterministic nonlinear ordinary and partial differential equations may admit chaotic behavior. Integrable differential equations possess certain structures that distinguish their solutions from the chaotic, and often display characteristics of both order and chaos for different values of the parameters. Distinguishing chaotic from integrable behavior is itself a difficult task that has led to invaluable insights into both chaotic and integrable systems.
The discretization of these systems has seen the emergence of many interesting examples of both discretely chaotic systems, such as chaotic maps, and discrete integrable systems, such as integrable difference equations. Many of the charac- terizations of chaotic and integrable dynamics possess discrete analogues. The techniques used to advance the theories of discrete chaotic and integrable systems have had origins in a broad range of mathematical disciplines, such as algebraic geometry, random matrix theory and representation theory.
The intersection of the theories pertaining to chaotic and integrable dynamics is a fertile ground for ideas for both of these areas. It is our aim to foster col- laboration between researchers. The interaction between the areas may lead to theory regarding the existence and stability of special solutions of chaotic systems, while interesting examples exhibiting seemingly chaotic behavior may be identified as possessing integrable behavior, leading to further developments in integrable dynamics.