ArticleOriginal scientific text

Title

Uniform pseudo-orbit tracing property for homeomorphisms and continuous mappings

Authors 1

Affiliations

  1. Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland

Abstract

We prove that for every nonempty compact manifold of nonzero dimension no self-homeomorphism and no continuous self-mapping has the uniform pseudo-orbit tracing property. Several relevant counterexamples for recently studied hypotheses are indicated.

Keywords

pseudo-orbit tracing property, discrete dynamical system on manifold, orbit stability

Bibliography

  1. R. Gu, Uniform pseudo-orbit tracing property and orbit stability, Ann. Differential Equations 13 (1997), 350-359.
  2. K. Odani, Generic homeomorphisms have the pseudo-orbit tracing property, Proc. Amer. Math. Soc. 110 (1990), 281-284.
  3. K. Sakai, The C1-uniform pseudo-orbit tracing property, Tokyo J. Math. 15 (1992), 99-109.
  4. K. Sakai, Pseudo-orbit tracing property and strong transversality of diffeomorphisms on closed manifolds, Osaka J. Math. 31 (1994), 373-386.
Pages:
1-6
Main language of publication
English
Received
1999-06-25
Accepted
2000-03-10
Published
2000
Exact and natural sciences