This handbook is volume II in a series collecting mathematical
state-of-the-art surveys in the field of dynamical systems. Much of
this field has developed from
interactions with other areas of science, and this volume shows how
concepts of dynamical systems further the understanding of
mathematical issues that arise in applications. Although modeling
issues are addressed, the central theme is the mathematically
rigorous investigation of the resulting differential equations and
their dynamic behavior. However, the authors and editors have made
an effort to ensure readability on a non-technical level for
mathematicians from other fields and for other scientists and
engineers.
The eighteen surveys collected here do not aspire to encyclopedic
completeness, but present selected paradigms. The surveys are
grouped into those emphasizing finite-dimensional methods,
numerics, topological methods, and partial differential equations.
Application areas include the dynamics of neural networks, fluid
flows, nonlinear optics, and many others.
While the survey articles can be read independently, they deeply
share recurrent themes from dynamical systems. Attractors,
bifurcations, center manifolds, dimension reduction, ergodicity,
homoclinicity, hyperbolicity, invariant and inertial manifolds,
normal forms, recurrence, shift dynamics, stability, to name
just a few, are ubiquitous dynamical concepts throughout the
articles.
General
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