Differentiably Ω-stable diffeomorphisms
Differentiably Ω-stable diffeomorphisms
复制标题
可微 Ω 稳定的微分同胚
DOI：
10.1016/0040-9383(72)90025-0
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发表时间：
1972
期刊：
影响因子：
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通讯作者：
J. Franks
中科院分区：
文献类型：
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作者：
J. Franks
如果在C ‘拓扑上存在一个邻域N，使得g EN意味着从L sZ （fl）的非游走集到g N (g)的非游走集的同胚p (g)满足0 cp (g)= q (g) 0j，则紧C ’流形的f: M-+ M称为q -稳定。& M)连续空间从Q映射到M，并且要求9是一个从N到C ' ' （QM）的函数，它在f处连续并且满足rp (f)= i，即从Q (f)映射到M的包含映射，则f称为强&mble。Smale [IO]为差分同态是强q稳定的提供了充分条件。这些条件是否必要是一个重要的悬而未决的问题。
A DIFFEOMORPHISM f: M-+ M of a compact C” manifold is called Q-stable if there is a neighborhood N offin the C’topology such that g EN implies there is a homeomorphism cp (g) from the non-wandering set of, L sZ (fl to the non-wandering set of g, n (g) which satisfiesg 0 cp (g)= q (g) 0JIf we consider C”(! & M) the space of continuous maps from Q to M and require that 9 be a function from N to C”(QM) which is continuous at f and satisfies rp (f)= i, the inclusion map from Q (f) to M, then f is called strongly &mble. Smale [IO] provides sufficient conditions for a diffeomorphism to be strongly Q-stable. Whether or not these conditions are necessary is an important open question.