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

Mathematics > Dynamical Systems

arXiv:2206.00353 (math)
[Submitted on 1 Jun 2022]

Title:Expansivity and strong structural stability for composition operators on $L^p$ spaces

Authors:Martina Maiuriello
View PDF
Abstract:In this note we investigate the two notions of expansivity and strong structural stability for composition operators on $L^p$ spaces, $1 \leq p < \infty$. Necessary and sufficient conditions for such operators to be expansive are provided, both in the general and the dissipative case. We also show that, in the dissipative setting, the shadowing property implies the strong structural stability and we prove that these two notions are equivalent under the extra hypothesis of positive expansivity.
Subjects: Dynamical Systems (math.DS)
MSC classes: Primary: 47B33, 37C20, Secondary: 37B05, 37B65
Cite as: arXiv:2206.00353 [math.DS]
  (or arXiv:2206.00353v1 [math.DS] for this version)
  https://doi.org/10.48550/arXiv.2206.00353

Submission history

From: Martina Maiuriello [view email]
[v1] Wed, 1 Jun 2022 09:38:26 UTC (24 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
view license
Current browse context:
math.DS
< prev   |   next >
new | recent | 2022-06
Change to browse by:
math

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?)