Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.01548 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917380023648256 |
|---|---|
| author | Kantic, Jonas Qureshi, Claudio Panario, Daniel Legl, Fabian |
| author_facet | Kantic, Jonas Qureshi, Claudio Panario, Daniel Legl, Fabian |
| contents | Linear finite dynamical systems play an important role, for example, in coding theory and simulations.
Methods for analyzing such systems are often restricted to cases in which the system
is defined over a field %and usually strive to achieve a complete description of the system and its dynamics.
or lack practicability to effectively analyze the system's dynamical behavior.
However, when analyzing and prototyping finite dynamical systems, it is often desirable to quickly obtain basic information such as
the length of cycles and transients that appear in its dynamics, which is reflected in the structure of the connected components
of the corresponding functional graphs.
In this paper, we extend the analysis of the dynamics of linear finite dynamical systems that act over cyclic modules to Galois rings.
Furthermore, we propose algorithms for computing the length of the cycles and the height of the trees that make up
their functional graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_01548 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Dynamics of Linear Finite Dynamical Systems Over Galois Rings Kantic, Jonas Qureshi, Claudio Panario, Daniel Legl, Fabian Dynamical Systems Data Structures and Algorithms Commutative Algebra Linear finite dynamical systems play an important role, for example, in coding theory and simulations. Methods for analyzing such systems are often restricted to cases in which the system is defined over a field %and usually strive to achieve a complete description of the system and its dynamics. or lack practicability to effectively analyze the system's dynamical behavior. However, when analyzing and prototyping finite dynamical systems, it is often desirable to quickly obtain basic information such as the length of cycles and transients that appear in its dynamics, which is reflected in the structure of the connected components of the corresponding functional graphs. In this paper, we extend the analysis of the dynamics of linear finite dynamical systems that act over cyclic modules to Galois rings. Furthermore, we propose algorithms for computing the length of the cycles and the height of the trees that make up their functional graphs. |
| title | On the Dynamics of Linear Finite Dynamical Systems Over Galois Rings |
| topic | Dynamical Systems Data Structures and Algorithms Commutative Algebra |
| url | https://arxiv.org/abs/2604.01548 |