Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 
 

 

An annulus diffeomorphism
with non-Denjoy minimal sets


Author: Mark Turpin
Journal: Proc. Amer. Math. Soc. 126 (1998), 1851-1856
MSC (1991): Primary 58F13
DOI: https://doi.org/10.1090/S0002-9939-98-04364-0
MathSciNet review: 1451833
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We construct an annulus diffeomorphism with the property that a countably dense set of irrational rotation numbers are represented only by pseudocircles on which the diffeomorphism acts minimally but is not semi-conjugate to rigid rotation on the circle. This answers a question of Boyland about whether such behavior is possible only at the maximum or minimum of the rotation set.


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

  • [B1] R.H. Bing, A homogeneous indecomposable plane continuum, Duke Math. J. 15 (1948), 729-742. MR 10:261a
  • [B2] -, Concerning hereditarily indecomposable continua, Pacific J. Math. 1 (1951), 43-51. MR 13:265b
  • [Bd] P. Boyland, The rotation set as a dynamical invariant, in: \underline{Twist Mappings and} \underline{Their Applications}, IMA Volumes in Mathematics, 44 ed. R. McGehee and K. Meyer (Springer, Berlin, 1992, pp. 73-86). MR 94i:58104
  • [D] R.L. Devaney, \underline{An Introduction to Chaotic Dynamical Systems}, (Benjamin/Cummings, 1986). MR 87e:58142
  • [F] L. Fearnley, The pseudo-circle is unique, Trans. Amer. Math. Soc. 149 (1970), 45-64. MR 41:6172
  • [H] M. Handel, A pathological area preserving $ C^{\infty} $ diffeomorphism of the plane, Proc. Amer. Math. Soc. 86 (1982), 163-168. MR 84f:58040
  • [M] J. Moser, Lectures on Hamiltonian systems, Mem. Amer. Math. Soc. 81(1968), 1-60. MR 37:6060
  • [T] M. Turpin, The restricted rotation number of an example of Handel, preprint.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 58F13

Retrieve articles in all journals with MSC (1991): 58F13


Additional Information

Mark Turpin
Affiliation: Department of Mathematics, University of Hartford, West Hartford, Connecticut 06117
Email: mturpin@hartford.edu

DOI: https://doi.org/10.1090/S0002-9939-98-04364-0
Received by editor(s): June 25, 1996
Received by editor(s) in revised form: November 1, 1996
Communicated by: Mary Rees
Article copyright: © Copyright 1998 American Mathematical Society

American Mathematical Society