Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Nonlinear Sciences > Chaotic Dynamics

arXiv:nlin/0302048 (nlin)
[Submitted on 20 Feb 2003 (v1), last revised 24 Oct 2004 (this version, v2)]

Title:Dynamics and computation in functional shifts

Authors:Jun Namikawa, Takashi Hashimoto
View PDF
Abstract: We introduce a new type of shift dynamics as an extended model of symbolic dynamics, and investigate the characteristics of shift spaces from the viewpoints of both dynamics and computation. This shift dynamics is called a functional shift that is defined by a set of bi-infinite sequences of some functions on a set of symbols. To analyze the complexity of functional shifts, we measure them in terms of topological entropy, and locate their languages in the Chomsky hierarchy. %Through this study, we argue that complexity of dynamics does not correspond to that of computation. Through this study, we argue that considering functional shifts from the viewpoints of both dynamics and computation give us opposite results about the complexity of systems. We also describe a new class of shift spaces whose languages are not recursively enumerable.
Comments: 23 pages, 2 figures
Subjects: Chaotic Dynamics (nlin.CD)
Cite as: arXiv:nlin/0302048 [nlin.CD]
  (or arXiv:nlin/0302048v2 [nlin.CD] for this version)
  https://doi.org/10.48550/arXiv.nlin/0302048
Journal reference: Nonlineality 17 pp.1317-1336 (2004)
Related DOI: https://doi.org/10.1088/0951-7715/17/4/009

Submission history

From: Jun Namikawa [view email]
[v1] Thu, 20 Feb 2003 08:45:35 UTC (17 KB)
[v2] Sun, 24 Oct 2004 15:01:59 UTC (43 KB)
Full-text links:

Access Paper:

view license
Current browse context:
nlin.CD
< prev   |   next >
new | recent | 2003-02

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

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

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

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.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)