C^1-stably positively expansive maps

• Autorzy: Sakai K.
• Języki publikacji: EN

Abstrakty

EN

The notion of C^1-stably positively expansive differentiable maps on closed C^infinity manifolds is introduced, and it is proved that a differentiable map f is C^1-stably positively expansive if and only if f is expanding. Furthermore, for such maps, the [epsilon]-time dependent stability is shown. As a result, every expanding map is e-time dependent stable.

Słowa kluczowe

EN

C^1-stably positively expansive; expanding; pseudo-orbit; shadowing property; time dependent stable

PL

stabilna zależność od czasu; układ dynamiczny; teoria ergodyczna; rozwinięcie dodatnie; rozwijanie

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2004
• Tom: Vol. 52, nr 2
• Strony: 197--209
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Sakai K.

Bibliografia

• [1] E. M. Coven and W. L. Reddy, Positively expansive maps of compact manifolds, in: Lecture Notes in Math. 819, Springer, Berlin, 1980, 96-110.
• [2] J. Franks, Necessary conditions for stability of diffeomorphisms, Trans. Amer. Math. Soc. 158 (1971), 301-308.
• [3] -, Time dependent stable diffeomorphisms, Invent. Math. 24 (1974), 163-172.
• [4] D. Ruelle, Thermodynamic Formalism, Encyclopedia Math. Appl. 5, Addison-Wesley, Reading, MA, 1978.
• [5] K. Sakai, Periodic points of positively expansive maps, Proc. Amer. Math. Soc. 94 (1985), 531-534.
• [6] -, Various shadowing properties for positively expansive maps, Topology Appl. 131 (2003), 15-31.
• [7] M. Shub, Endomorphisms of compact differentiable manifolds, Amer. J. Math. 91 (1969), 175-199.
• [8] P. Walters, On the pseudo orbit tracing property and its relationship to stability, in: Lecture Notes in Math. 668, Springer, Berlin, 1978, 231-244.