Uniform pseudo-orbit tracing property for homeomorphisms and continuous mappings

• Autorzy: Marcin Kulczycki
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2000
• Tom: 75
• Numer: 1
• Strony: 1-6

Daty

wydano

2000

otrzymano

1999-06-25

poprawiono

2000-03-10

Twórcy

autor

Marcin Kulczycki

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

Bibliografia

• [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 $C^1$-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.