2010/06/22 by Berger, Pierre, Rovella, Alvaro · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.1006.4302
We present several results suggesting that the concept of C1-inverse limit stability is free of singularity theory. We describe an example of a C1-inverse stable endomorphism which is robustly transitive with persistent critical set. We show that every (weak) axiom A, C1-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 C1-inverse limit stable. The latter is applied to Hénon maps, rational functions of the sphere and others. This leads us to conjecture that C1-inverse stable endomorphisms are those which satisfy axiom A and the strong transversality condition (T).