Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perbaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van GuIik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related.
Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
Brief Introduction to the Contents of the Book.- Reduction of the Dynamics of a Bifurcation Problem Using Normal Forms and Symmetries.- Stable Cycles with Complicated Structure.- Large Scale Instabilities of Cellular Flows.- Physical Interpretation of Optical Bifurcations.- The Interaction of Sound and Vorticity.- Spatio-Temporal Instabilities in Closed and Open Flows.- Models of Pattern Formation from a Singularity Theory Point of View.- Patterns and Defects Far from Equilibrium.- Nonequilibrium Correlation Functions.- Fluctuations in Unstable Systems.- Weak Noise Limit and Nonequilibrium Potentials of Dissipative Dynamical Systems.- Fluctuations in "Metastable" Systems.- Normal Forms with Noise.- Adiabatic Nucleation, Stability Limit and the Glass Transition Temperature.- Magnetic Islands Created by Resonant Helical Windings.- A Non-Markovian Lorentz Gas Model.