Next Article in Journal
Periodic Solution and Asymptotic Stability for the Magnetohydrodynamic Equations with Inhomogeneous Boundary Condition
Next Article in Special Issue
Relation Theoretic Common Fixed Point Results for Generalized Weak Nonlinear Contractions with an Application
Previous Article in Journal
The Monotonic Sequence Theorem and Measurement of Lengths and Areas in Axiomatic Non-Standard Hyperrational Analysis
Previous Article in Special Issue
Fixed Point Theorems for Geraghty Contraction Type Mappings in b-Metric Spaces and Applications
Article Menu

Export Article

Open AccessArticle

Applications of Square Roots of Diffeomorphisms

Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan
Axioms 2019, 8(2), 43;
Received: 9 March 2019 / Revised: 8 April 2019 / Accepted: 9 April 2019 / Published: 11 April 2019
(This article belongs to the Special Issue Fixed Point Theory and Related Topics)
PDF [220 KB, uploaded 11 April 2019]


In this paper, we prove that on any contact manifold ( M , ξ ) there exists an arbitrary C -small contactomorphism which does not admit a square root. In particular, there exists an arbitrary C -small contactomorphism which is not “autonomous”. This paper is the first step to study the topology of C o n t 0 ( M , ξ ) Aut ( M , ξ ) . As an application, we also prove a similar result for the diffeomorphism group Diff ( M ) for any smooth manifold M. View Full-Text
Keywords: diffeomorphism; contactomorphism; symplectomorphism diffeomorphism; contactomorphism; symplectomorphism
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

Sugimoto, Y. Applications of Square Roots of Diffeomorphisms. Axioms 2019, 8, 43.

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