自覆盖映射的双曲极限集

HYPERBOLIC LIMIT SETS OF A COVERING MAPPING

在微分动力系统Ω-稳定性的研究中,S.Smale等人证明了:公理A+无环条件(?)Ω-稳定。S.E.Newhouse减弱了此结论的条件,得出f的α-极限点集的闭包是双曲的且满足无环条件,则f满足公理A,从而f是Ω-稳定的([1])。 文献[3]证明了满足公理A及无环条件的自覆盖映射是Ω-单一化稳定的。本文将此结论的条件减弱,得出与[1]相应的结论(定理2)。

In this paper we consider the covering mapping of a compact manifold M,and prove that if the closure of the a-limit set of f, denoted by L^(-1)(f),is hyperbolic and does not admit of cycles,then f statisfies Axiom A and has no cycles,and therefore f is orbit shift Ω-stable.