Modeling and computations in dynamical systems : in commemoration of the 100th anniversary of the birth of John von Neumann ; [papers ... based on lectures presented at the October 2003 Budapest Workshop on Modeling and Computations in Dynamical Systems

The Hungarian born mathematical genius, John von Neumann, was undoubtedly one of the greatest and most influential scientific minds of the 20th century. Von Neumann made fundamental contributions to Computing and he had a keen interest in Dynamical Systems, specifically Hydrodynamic Turbulence. This book, offering a state-of-the-art collection of papers in computational dynamical systems, is dedicated to the memory of von Neumann. Including contributions from J E Marsden, P J Holmes, M Shub, A Iserles, M Dellnitz and J Guckenheimer, this book offers a unique combination of theoretical and applied research in areas such as geometric integration, neural networks, linear programming, dynamical astronomy, chemical reaction models, structural and fluid mechanics.The contents of this book was also published as a special issue of the International Journal of Bifurcation and Chaos — March 2005. 3. The Main Result: The Conditions for Am =BMN4. Application of the Coarse-Grained Model; 5. Summary and Related Topics; Multiple Helical Perversions of Finite Intristically Curved Rods; 1. Introduction; 2. Analysis; 3. Global Computations and their Interpretation; 4. Summary and Related Issues; Bifurcations of Stable Sets in Noninvertible Planar Maps; 1. Introduction; 2. Example; 3. Generic Codimension-One Bifurcations of Stable Sets; 4. Bifurcations of Basin Boundaries; 5. Stable Set versus Unstable Manifold; 6. Conclusions; Multiparametric Bifurcations in an Enzyme-Catalyzed Reaction Model Commutators of Skew-Symmetric Matrices1. Norms and Commutators in Mn[R] and sO(n); 2. The Reduced Commutator Matrix in so(n); 3. The Radius of so(n) for n> 4; 4. Conclusion; Simple Neural Networks that Optimize Decisions; 1. Introduction; 2. Models of Decision Tasks; 3. Optimal Signal Discrimination in the One-Dimensional Models; 4. The Locus Coeruleus Brainstem Area and Optimal Gain Trajectories; 5. Discussion and Conclusions; Newton Flow and Interior Point Methods in Linear Programming; 1. Introduction; 2. The Central Path is a Trajectory of the Newton Vector Field 3. An Analytic Expression for the Newton Vector Field4. Extension to the Faces of p; 5. Analyticity and Derivatives; 6. Example; Numerical Continuation of Branch Points of Equilibria and Periodic Orbits; 1. Introduction; 2. Equilibria and their Branch Points; 3. Periodic Solutions and their Branch Points; 4. Numerical Detection Computation and Continuation of Branch Points of Periodic Solutions; 5. Example 1: The A -> B -> C Reaction; 6. Example 2: An Electronic Circuit; Coarse-Grained Observation of Discretized Maps; 1. Introduction; 2. Definitions and Assumptions Bifurcations and Continuous Transitions of Attractors in Autonomous and Nonautcnomcus Systems1. Introduction; 2. Autonomous Systems; 3. Nonautonomous Systems; 4. A Total Stability Theorem; 5. Applications of the Total Stability Theorem; 6. Concluding Remarks and Questions; A. Appendix: Proof of Theorem 1; A Survey of Methods for Computing (Un)Stable Manifolds of Vector Fields; 1. Introduction; 2. Approximation by Geodesic Level Sets; 3. BVP Continuation of Trajectories; 4. Computation of Fat Trajectories; 5. PDE Formulation; 6. Box Covering; 7. Discussion Offers a collection of papers in computational dynamical systems, dedicated to the memory of John von Neumann. This book offers a combination of theoretical and applied research in areas such as geometric integration, neural networks, linear programming, dynamical astronomy, chemical reaction models, structural and fluid mechanics.