Whenever systems are governed by continuous chains of causes and
effects, their behavior exhibits the consequences of dynamical
symmetries, many of them far from obvious. Dynamical Symmetry
introduces the reader to Sophus Lie's discoveries of the
connections between differential equations and continuous groups
that underlie this observation. It develops and applies the
mathematical relations between dynamics and geometry that result.
Systematic methods for uncovering dynamical symmetries are
described, and put to use. Much material in the book is new and
some has only recently appeared in research journals.Though Lie
groups play a key role in elementary particle physics, their
connection with differential equations is more often exploited in
applied mathematics and engineering. Dynamical Symmetry bridges
this gap in a novel manner designed to help readers establish new
connections in their own areas of interest. Emphasis is placed on
applications to physics and chemistry. Applications to many of the
other sciences illustrate both general principles and the
ubiquitousness of dynamical symmetries.
General
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