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.

Contents:

• Transport in Dynamical Astronomy and Multibody Problems (M Dellnitz et al.)
• A Brief Survey on the Numerical Dynamics for Functional Differential Equations (B M Garay)
• Bifurcations and Continuous Transitions of Attractors in Autonomous and Nonautonomous Systems (P E Kloeden & S Siegmund)
• A Survey of Methods for Computing (Un)Stable Manifolds of Vector Fields (B Krauskopf et al.)
• Commutators of Skew-Symmetric Matrices (A M Bloch & A Iserles)
• Simple Neural Networks that Optimize Decisions (E Brown et al.)
• Newton Flow and Interior Point Methods in Linear Programming (J-P Dedieu & M Shub)
• Numerical Continuation of Branch Points of Equilibria and Periodic Orbits (E J Doedel et al.)
• Coarse-Grained Observation of Discretized Maps (G Domokos)
• Multiple Helical Perversions of Finite, Intristically Curved Rods (G Domokos & T J Healey)
• Bifurcations of Stable Sets in Noninvertible Planar Maps (J P England et al.)
• Multiparametric Bifurcations in an Enzyme-Catalyzed Reaction Model (E Freire et al.)
• Straightforward Computation of Spatial Equilibria of Geometrically Exact Cosserat Rods (T J Healey & P G Mehta)
• Multiparameter Parallel Search Branch Switching (M E Henderson)
• Equation-Free, Effective Computation for Discrete Systems: A Time Stepper Based Approach (J Möller et al.)
• Model Reduction for Fluids, Using Balanced Proper Orthogonal Decomposition (C W Rowley)
• Bifurcation Tracking Algorithms and Software for Large Scale Applications (A G Salinger et al.)
• An Algorithm for Finding Invariant Algebraic Curves of a Given Degree for Polynomial Planar Vector Fields (G Swirszcz)