Mathematics > Dynamical Systems
[Submitted on 13 Mar 2025
]
Title: Elementary fractal geometry. 6. The dynamical interior of self-similar sets
Title: 初等分形几何。 6. 自相似集的动力内部
Abstract: On the one hand, the dynamical interior of a self-similar set with open set condition is the complement of the dynamical boundary. On the other hand, the dynamical interior is the recurrent set of the magnification flow. For a finite type self-similar set, both boundary and interior are described by finite automata. The neighbor graph defines the boundary. The neighborhood graph, based on work by Thurston, Lalley, Ngai and Wang, defines the interior. If local views are considered up to similarity, the interior obtains a discrete manifold structure, and the magnification flow is discretized by a Markov chain. This leads to new methods for the visualization and description of finite type attractors.
Submission history
From: Christoph Bandt [view email][v1] Thu, 13 Mar 2025 14:52:53 UTC (19,206 KB)
Bibliographic and Citation Tools
Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)
Code, Data and Media Associated with this Article
alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)
Demos
Recommenders and Search Tools
Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)
IArxiv Recommender
(What is IArxiv?)
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.