التفاصيل البيبلوغرافية
| العنوان: |
Symbolic extensions and dominated splittings for generic $$C^{1}$$C1-diffeomorphisms. |
| المؤلفون: |
Arbieto, A., Armijo, A., Catalan, T., Senos, L. |
| المصدر: |
Mathematische Zeitschrift; Dec2013, Vol. 275 Issue 3/4, p1239-1254, 16p |
| مستخلص: |
Let $$\mathrm{Diff }^1(M)$$ Diff 1 ( M ) be the set of all $$C^1$$ C 1 -diffeomorphisms $$f:M\rightarrow M$$ f : M → M , where $$M$$ M is a compact boundaryless d-dimensional manifold, $$d\ge 2$$ d ≥ 2 . We prove that there is a residual subset $$\mathfrak R $$ R of $$\mathrm{Diff }^1(M)$$ Diff 1 ( M ) such that if $$f\in \mathfrak R $$ f ∈ R and if $$H(p)$$ H ( p ) is the homoclinic class associated with a hyperbolic periodic point $$p$$ p , then either $$H(p)$$ H ( p ) admits a dominated splitting of the form $$E\oplus F_1\oplus \dots \oplus F_k\oplus G$$ E ⊕ F 1 ⊕ … ⊕ F k ⊕ G , where $$F_i$$ F i is not hyperbolic and one-dimensional, or $$f|_{H(p)}$$ f | H ( p ) has no symbolic extensions. [ABSTRACT FROM AUTHOR] |
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| قاعدة البيانات: |
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