Unfolding contracting singular cycles. (English) Zbl 0802.58036

Pacifico, M. J.; Rovella, A.

Ann. Sci. Éc. Norm. Supér. (4) 26, No. 6, 691-700 (1993).

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”.

Reviewer: C.Chicone (Columbia)

MSC:

37D15	Morse-Smale systems
37D99	Dynamical systems with hyperbolic behavior

Keywords:

Morse-Smale vector field; singular cycle; hyperbolic flows

References:

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