Uniform pseudo-orbit tracing property for homeomorphisms and continuous mappings

Marcin Kulczycki

Annales Polonici Mathematici (2000)

  • Volume: 75, Issue: 1, page 1-6
  • ISSN: 0066-2216

Abstract

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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.

How to cite

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Kulczycki, Marcin. "Uniform pseudo-orbit tracing property for homeomorphisms and continuous mappings." Annales Polonici Mathematici 75.1 (2000): 1-6. <http://eudml.org/doc/208381>.

@article{Kulczycki2000,
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.},
author = {Kulczycki, Marcin},
journal = {Annales Polonici Mathematici},
keywords = {pseudo-orbit tracing property; discrete dynamical system on manifold; orbit stability; axiom A},
language = {eng},
number = {1},
pages = {1-6},
title = {Uniform pseudo-orbit tracing property for homeomorphisms and continuous mappings},
url = {http://eudml.org/doc/208381},
volume = {75},
year = {2000},
}

TY - JOUR
AU - Kulczycki, Marcin
TI - Uniform pseudo-orbit tracing property for homeomorphisms and continuous mappings
JO - Annales Polonici Mathematici
PY - 2000
VL - 75
IS - 1
SP - 1
EP - 6
AB - 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.
LA - eng
KW - pseudo-orbit tracing property; discrete dynamical system on manifold; orbit stability; axiom A
UR - http://eudml.org/doc/208381
ER -

References

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  1. [1] R. Gu, Uniform pseudo-orbit tracing property and orbit stability, Ann. Differential Equations 13 (1997), 350-359. Zbl0906.58021
  2. [2] K. Odani, Generic homeomorphisms have the pseudo-orbit tracing property, Proc. Amer. Math. Soc. 110 (1990), 281-284. Zbl0713.58025
  3. [3] K. Sakai, The C 1 -uniform pseudo-orbit tracing property, Tokyo J. Math. 15 (1992), 99-109. Zbl0763.58022
  4. [4] K. Sakai, Pseudo-orbit tracing property and strong transversality of diffeomorphisms on closed manifolds, Osaka J. Math. 31 (1994), 373-386. Zbl0820.58045

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