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
 
 
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Article

Diffeomorphisms with Shadowable Measures

1
Department of Mathematics, Tokushima University, Tokushima 770-8502, Japan
2
Department of Mathematics, Utsunomiya University, Utsunomiya 321-8505, Japan
3
Department of Mathematics, Kumamoto University, Kumamoto 860-8555, Japan
*
Author to whom correspondence should be addressed.
Axioms 2018, 7(4), 93; https://doi.org/10.3390/axioms7040093
Submission received: 8 November 2018 / Accepted: 5 December 2018 / Published: 7 December 2018
(This article belongs to the Special Issue Shadowing in Dynamical Systems)

Abstract

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.
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

Share and Cite

MDPI and ACS Style

Moriyasu, K.; Sakai, K.; Sumi, N. Diffeomorphisms with Shadowable Measures. Axioms 2018, 7, 93. https://doi.org/10.3390/axioms7040093

AMA Style

Moriyasu K, Sakai K, Sumi N. Diffeomorphisms with Shadowable Measures. Axioms. 2018; 7(4):93. https://doi.org/10.3390/axioms7040093

Chicago/Turabian Style

Moriyasu, Kazumine, Kazuhiro Sakai, and Naoya Sumi. 2018. "Diffeomorphisms with Shadowable Measures" Axioms 7, no. 4: 93. https://doi.org/10.3390/axioms7040093

APA Style

Moriyasu, K., Sakai, K., & Sumi, N. (2018). Diffeomorphisms with Shadowable Measures. Axioms, 7(4), 93. https://doi.org/10.3390/axioms7040093

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop