Form Symmetries and Reduction of Order in Difference Equations

As the field of difference equations expands, the discovery of general new methods of study and analysis can aid considerably in the evolution of the subject. This book presents a new systematic approach to reduction of order by changing variables. The author builds a step-by-step framework by defining the context for a formalization based on semiconjugacy and then presenting results for large classes of difference equations to which the new methods apply. The text shows that the characteristic polynomial and both the complimentary and particular solutions can be calculated directly from additively separable form symmetries of a larger class of difference equations.