English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

The scalar difference equation $x_{n+1}=f_{n}(x_{n},x_{n-1},...,x_{n-k})$ mayexhibit symmetries in its form that allow for reduction of order throughsubstitution or a change of variables. Such form symmetries can be definedgenerally using the semiconjugate relation on a group which yields a reductionof order through the semiconjugate factorization of the difference equation oforder $k+1$ into equations of lesser orders. Different classes of equations areconsidered including separable equations and homogeneous equations of degree 1.Applications include giving a complete factorization of the linearnon-homogeneous difference equation of order $k+1$ into a system of $k+1$ firstorder linear non-homogeneous equations in which the coefficients are theeigenvalues of the higher order equation. Form symmetries are also used toexplain the complicated multistable behavior of a separable, second orderexponential equation.

Order-reducing Form Symmetries and Semiconjugate Factorizations of Difference Equations