On recurrence equations associated with invariant varieties of periodic points

TL;DR

This paper explores how recurrence equations, which are discrete integrable equations with fixed-period solutions, can be derived from invariant varieties of periodic points in higher-dimensional integrable maps.

Contribution

It demonstrates that infinitely many recurrence equations can be constructed from the invariant varieties of periodic points in higher-dimensional integrable systems.

Findings

Infinite recurrence equations can be derived from invariant varieties.

Solutions of these equations are all periodic with fixed periods.

The approach links recurrence equations to geometric structures of integrable maps.

Abstract

A recurrence equation is a discrete integrable equation whose solutions are all periodic and the period is fixed. We show that infinitely many recurrence equations can be derived from the information about invariant varieties of periodic points of higher dimensional integrable maps.