Next Article in Journal
A Metric for Finite Power Multisets of Positive Real Numbers Based on Minimal Matching
Next Article in Special Issue
Relations between Shadowing and Inverse Shadowing in Dynamical Systems
Previous Article in Journal
Regional Enlarged Observability of Fractional Differential Equations with Riemann—Liouville Time Derivatives
Previous Article in Special Issue
Equicontinuity, Expansivity, and Shadowing for Linear Operators
Article Menu

Export Article

Open AccessArticle
Axioms 2018, 7(4), 93;

Diffeomorphisms with Shadowable Measures

Department of Mathematics, Tokushima University, Tokushima 770-8502, Japan
Department of Mathematics, Utsunomiya University, Utsunomiya 321-8505, Japan
Department of Mathematics, Kumamoto University, Kumamoto 860-8555, Japan
Author to whom correspondence should be addressed.
Received: 8 November 2018 / Accepted: 5 December 2018 / Published: 7 December 2018
(This article belongs to the Special Issue Shadowing in Dynamical Systems)
Full-Text   |   PDF [239 KB, uploaded 7 December 2018]   |  


In this paper, the notion of shadowable measures is introduced as a generalization of the shadowing property from the measure theoretical view point, and the set of diffeomorphisms satisfying the notion is considered. The dynamics of the C 1 -interior of the set of diffeomorphisms possessing the shadowable measures is characterized as the uniform hyperbolicity. View Full-Text
Keywords: shadowing property; pseudo-orbit; shadowable measure; Axiom A; no-cycle condition; strong transversality condition shadowing property; pseudo-orbit; shadowable measure; Axiom A; no-cycle condition; strong transversality condition

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

Share & Cite This Article

MDPI and ACS Style

Moriyasu, K.; Sakai, K.; Sumi, N. Diffeomorphisms with Shadowable Measures. Axioms 2018, 7, 93.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Axioms EISSN 2075-1680 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top