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)

 
 

 

Nonexistence of positively expansive maps on compact connected manifolds with boundary


Author: Koichi Hiraide
Journal: Proc. Amer. Math. Soc. 110 (1990), 565-568
MSC: Primary 54H20; Secondary 34C35, 54C20, 54E40, 58F15
DOI: https://doi.org/10.1090/S0002-9939-1990-1019272-1
MathSciNet review: 1019272
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this note we prove that no compact connected manifold with boundary admits a positively expansive map.


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

  • [1] N. Aoki and K. Hiraide, Dynamical systems of self-covering maps of the tori, preprint.
  • [2] E. M. Coven and W. L. Reddy, Positively expansive maps of compact manifolds, Lecture Notes in Math., vol. 819, Springer-Verlag, Berlin and New York, 1980, pp. 96-110. MR 591178 (82h:58024)
  • [3 D] W. Curtis and S. Miklos, Nonexistence of local expansions on certain continua, Fund. Math. 129 (1988), 207-210. MR 962542 (89k:54031)
  • [4] J. Franks, Anosov diffeomorphisms, Global Anal., Proc. Sympos. Pure Math., vol. 14, Amer. Math. Soc., Providence, RI, 1970, pp. 61-93. MR 0271990 (42:6871)
  • [5] W. H. Gottschalk and G. A. Hedlund, Topological dynamics, Amer. Math. Soc. Colloq, Publ., vol. 36, Amer. Math. Soc., Providence, RI, 1955. MR 0074810 (17:650e)
  • [6] M. Gromov, Groups of polynomial growth and expanding maps, Inst. Hautes Études Sci. Publ. Math. 53 (1981), 53-78. MR 623534 (83b:53041)
  • [7] D. W. Hall and G. L. Spencer II, Elementary topology, Wiley, New York, 1955. MR 0074804 (17:649a)
  • [8] K. Hiraide, Positively expansive maps and growth of fundamental groups, Proc. Amer. Math. Soc. 104 (1988), 934-941. MR 964877 (90a:57028)
  • [9] M. W. Hirsch, Expanding maps and transformation groups, Global Anal., Proc. Sympos. Pure Math., vol. 14, Amer. Math. Soc., Providence, RI, 1970, pp. 125-131. MR 0298701 (45:7750)
  • [10] W. L. Reddy, Expanding maps on compact metric spaces, Topology Appl. 13 (1982), 327-334. MR 651514 (83d:54070)
  • [11] M. Shub, Endomorphisms of compact differentiable manifolds, Amer. J. Math. 91 (1969), 175-199. MR 0240824 (39:2169)
  • [12] -, Expanding maps, Global Anal., Proc. Sympos. Pure Math., vol. 14, Amer. Math. Soc., Providence, RI, 1970, pp. 273-276. MR 0266251 (42:1158)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54H20, 34C35, 54C20, 54E40, 58F15

Retrieve articles in all journals with MSC: 54H20, 34C35, 54C20, 54E40, 58F15


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1990-1019272-1
Keywords: Positively expansive map, manifold with boundary, infra-nil-manifold
Article copyright: © Copyright 1990 American Mathematical Society

American Mathematical Society