The goal of the workshop was to provide a platform for an interdisciplinary exchange between researchers in economics and mathematics to push forward the understanding of global properties of economic dynamics. This included the discussion of new analytical and numerical tools that help to better address relevant economic questions in that field as well as the presentation of applications of global stability analyses in different areas of economic research. Besides taking stock of recent developments the meeting aimed at identifying the key challenges of this line of research and the most promising directions to proceed. The workshop also provided a platform for discussions of several important issues that have received only limited attention in previous work in the area, like the importance of the analysis of the basins of attraction of co-existing equilibria for the evaluation of economic policy measures or conceptual issues with respect to the choice between discrete versus continuous time models.
There was strong interest of researchers in several fields for this meeting. The workshop programme consisted of three plenary and 21 regular talks and almost 40 participants from Europe, USA, Asia and Australia attended the workshop. The scope of papers presented ranged from applications of global analysis in Finance, Industrial Organization, Growth Theory and Monetary Policy to technical issues like the global analysis of piece-wise smooth dynamical systems. The three plenary talks addressed quite distinct promising areas of research in nonlinear economic dynamics. Gustav Feichtinger gave a survey over recent work dealing with the characterization of optimal paths and basins of attractions in infinite horizon optimal control problems with coexisting attractors. In such problems there is history dependence in the sense that the long run outcome of the optimally controlled economic system depends on its initial state and for certain initial conditions the optimal policy is not unique. Gustav Feichtinger discussed extensions of initial work in one-dimensional problems to higher dimensions and illustrated the economic relevance of this type of analysis with several examples. He also pointed out several conceptual issues that arise in cases where the policy maker is for certain initial conditions indifferent between several different paths that all end up at the same attractor. Research in this area relies heavily on the application of suitable numerical methods for the determination of threshold points or curves and also these aspects were discussed in the talk. In the second plenary talk Richard Day stressed the importance of the consideration of structural change and potential structural instability when analysing macroeconomic dynamics and economic growth. Relying on a rich set of historical examples he argued that growth models should take into account issues like minimal subsistence requirements and the associated potential for non-continuous structural changes. Using a simple example of a growth model with minimal consumption requirements he showed that the behaviour of the resulting multi-regime dynamical system might substantially deviate from standard results. The final plenary talk by Tönu Puu focused on challenges of global analysis in dynamic economics. He argued that the new methods that recently became available allow for rigorous analyses of many issues that have been raised since the 1920s but previously could not be properly addressed using dynamic models. This claim was illustrated with examples from spatial economics and oligopoly dynamics.