%0 Journal Article
%T Applications of Square Roots of Diffeomorphisms
%A Yoshihiro Sugimoto
%J -
%D 2019
%R https://doi.org/10.3390/axioms8020043
%X Abstract In this paper, we prove that on any contact manifold ( M , ¦Î ) there exists an arbitrary C ¡Ş -small contactomorphism which does not admit a square root. In particular, there exists an arbitrary C ¡Ş -small contactomorphism which is not ¡°autonomous¡±. This paper is the first step to study the topology of C o n t 0 ( M , ¦Î ) £¿ Aut ( M , ¦Î ) . As an application, we also prove a similar result for the diffeomorphism group Diff ( M ) for any smooth manifold M. View Full-Tex
%K diffeomorphism
%K contactomorphism
%K symplectomorphism
%U https://www.mdpi.com/2075-1680/8/2/43