关于自同态的逆极限稳定性
On the inverse limit stability of endomorphisms
摘要：
我们提出了几个结果表明，$C^1$ -逆极限稳定的概念是免费的奇异性理论。我们描述了一个$C^1$ -逆稳定自同态的例子，它是鲁棒传递的持久临界集。证明了每个（弱）公理A，$C^1$ -逆极限稳定自同态满足一定的强横截性条件$(T)$ .证明了满足公理A和条件$(T)$的吸引-排斥自同态是$C^1$ -逆极限稳定的.后者适用于Hénon地图，有理函数的领域和其他人。这使我们猜想$C^1$ -逆稳定自同态是满足公理A和强横截条件$(T)$的自同态.
英文摘要：
We present several results suggesting that the concept of $C^1$-inverse limit stability is free of singularity theory. We describe an example of a $C^1$-inverse stable endomorphism which is robustly transitive with persistent critical set. We show that every (weak) axiom A, $C^1$-inverse limit stable endomorphism satisfies a certain strong transversality condition $(T)$. We prove that every attractor-repellor endomorphism satisfying axiom A and Condition $(T)$ is $C^1$-inverse limit stable. The latter is applied to Hénon maps, rational functions of the sphere and others. This leads us to conjecture that $C^1$-inverse stable endomorphisms are those which satisfy axiom A and the strong transversality condition $(T)$.
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