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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.08387 |
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Table of Contents:
- We show that if any four distinct solutions of a rational difference equation are algebraically independent, then any number of distinct solutions to the equation are independent. A nontrivial variant of this result is given for autonomous difference equations or algebraic dynamical systems, where we show the degree of nonminimality is at most one. The results have a natural interpretation in terms of invariant or periodic subvarieties of algebraic dynamical systems and $σ$-varieties. Surprisingly, the proofs of these results rely on the classification of finite simple groups.