Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A pathological area preserving $ C\sp{\infty }$ diffeomorphism of the plane

Author: Michael Handel
Journal: Proc. Amer. Math. Soc. 86 (1982), 163-168
MSC: Primary 58E99; Secondary 28D05, 54F20, 58F12
MathSciNet review: 663889
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The pseudocircle $ P$ is an hereditarily indecomposable planar continuum. In particular, it is connected but nowhere locally connected. We construct a $ {C^\infty }$ area preserving diffeomorphism of the plane with $ P$ as a minimal set. The diffeomorphism $ f$ is constructed as an explicit limit of diffeomorphisms conjugate to rotations about the origin. There is a well-defined irrational rotation number for $ f\vert P$ even though $ f\vert P$ is not even semi-conjugate to a rotation of $ {S^1}$. If we remove the requirement that our diffeomorphisms be area preserving, we may alter the example so that $ P$ is an attracting minimal set.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 58E99, 28D05, 54F20, 58F12

Retrieve articles in all journals with MSC: 58E99, 28D05, 54F20, 58F12

Additional Information

Article copyright: © Copyright 1982 American Mathematical Society