Non existence of attractors and dynamics around some wild homoclinic classes

Details Non existence of attractors and dynamics around some wild homoclinic classes Non existence of attractors and dynamics around some wild homoclinic classes

2010-03-11

arxiv.org/abs/1003.2280v2

Mathematics

Dynamical Systems

14 pages. Some remarks added

Scientific paper

We present new examples of generic diffeomorphisms without attractors. Also, we study how these wild classes are accumulated by infinitely many other classes (obtaining that the chain recurrence classes different from the only quasi-attractor are contained in center stable manifolds). The construction relies on some derived from Anosov (DA) constructions and uses strongly the semiconjugacy obtained by these diffeomorphisms. An interesting feature of this examples is that we can show that robustly, they present a unique attractor in the sense of Milnor.

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