1st Edition
Form Symmetries and Reduction of Order in Difference Equations
Introduction
Difference Equations on Groups
Basic definitions
One equation, many interpretations
Examples of difference equations on groups
Semiconjugate Factorization and Reduction of Order
Semiconjugacy and ordering of maps
Form symmetries and SC factorizations
Order-reduction types
SC factorizations as triangular systems
Order-preserving form symmetries
Homogeneous Equations of Degree One
Homogeneous equations on groups
Characteristic form symmetry of HD1 equations
Reductions of order in HD1 equations
Absolute value equation
Type-(k,1) Reductions
Invertible-map criterion
Identity form symmetry
Inversion form symmetry
Discrete Riccati equation of order two
Linear form symmetry
Difference equations with linear arguments
Field-inverse form symmetry
Type-(1,k) Reductions
Linear form symmetry revisited
Separable difference equations
Equations with exponential and power functions
Time-Dependent Form Symmetries
The semiconjugate relation and factorization
Invertible-map criterion revisited
Time-dependent linear form symmetry
SC factorization of linear equations
Nonrecursive Difference Equations
Examples and discussion
Form symmetries, factors, and cofactors
Semi-invertible map criterion
Quadratic difference equations
An order-preserving form symmetry
Appendix: Asymptotic Stability on the Real Line
References
Index
Notes and Problems appear at the end of each chapter.
Biography
Hassan Sedaghat is a professor of mathematics at Virginia Commonwealth University. His research interests include difference equations and discrete dynamical systems and their applications in mathematics, economics, biology, and medicine.
This book presents a new approach to the formulation and study of difference equations. … The book is well organized. It is addressed to a broad audience in difference equations.
—Vladimir Sh. Burd, Mathematical Reviews, 2012e
