Unfolding contracting singular cycles. (English) Zbl 0802.58036

The authors’ abstract: “We show that if we start with a Morse-Smale vector field and move through a generic one-parameter family of vector fields to a contracting singular cycle and beyond, we reach a region filled up mostly with hyperbolic flows: the Lebesgue measure of parameter values corresponding to non-Axiom \(A\) flows is zero”.


37D15 Morse-Smale systems
37D99 Dynamical systems with hyperbolic behavior
Full Text: DOI Numdam EuDML


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