×

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”.

MSC:

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

References:

[1] R. BAMÓN , R. LABARCA , R. MAÑ;É and M. J. PACIFICO , The Explosion of Singular Cycles (to appear at Publ. Math. IHES). Numdam | Zbl 0801.58010 · Zbl 0801.58010
[2] M. HIRSCH , C. PUGH and M. SHUB , Invariant Manifolds (Lecture Notes in Mathematics, Vol. 583, Springer-Verlag, 1977 ). MR 58 #18595 | Zbl 0355.58009 · Zbl 0355.58009
[3] R. LABARCA and M. J. PACIFICO , Stability of Singular Horseshoes (Topology, Vol. 25, n^\circ 3, 1986 ). MR 87h:58106 | Zbl 0611.58033 · Zbl 0611.58033
[4] A. ROVELLA , The Dynamics of Perturbations of the Contracting Lorenz Attractor (Thesis, IMPA and to appear at Bol. Soc. Bras. Mat.). Zbl 0797.58051 · Zbl 0797.58051
[5] S. SINGER , Stable Orbits and Bifurcations of Maps of the Interval (SIAM, J. Appl. Math., Vol. 35, 1978 ). MR 58 #13206 | Zbl 0391.58014 · Zbl 0391.58014
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.