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Form Symmetries and Reduction of Order in Difference Equations (Paperback)
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Form Symmetries and Reduction of Order in Difference Equations (Paperback)
Series: Advances in Discrete Mathematics and Applications
Expected to ship within 12 - 17 working days
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Form Symmetries and Reduction of Order in Difference Equations
presents a new approach to the formulation and analysis of
difference equations in which the underlying space is typically an
algebraic group. In some problems and applications, an additional
algebraic or topological structure is assumed in order to define
equations and obtain significant results about them. Reflecting the
author's past research experience, the majority of examples involve
equations in finite dimensional Euclidean spaces. The book first
introduces difference equations on groups, building a foundation
for later chapters and illustrating the wide variety of possible
formulations and interpretations of difference equations that occur
in concrete contexts. The author then proposes a systematic method
of decomposition for recursive difference equations that uses a
semiconjugate relation between maps. Focusing on large classes of
difference equations, he shows how to find the semiconjugate
relations and accompanying factorizations of two difference
equations with strictly lower orders. The final chapter goes beyond
semiconjugacy by extending the fundamental ideas based on form
symmetries to nonrecursive difference equations. With numerous
examples and exercises, this book is an ideal introduction to an
exciting new domain in the area of difference equations. It takes a
fresh and all-inclusive look at difference equations and develops a
systematic procedure for examining how these equations are
constructed and solved.
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