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References (14)
-
L. Díaz, J. Rocha (1992)
Nonconnected heterodimensional cycles: bifurcation and stabilityNonlinearity, 5
-
Marek Rychlik (1990)
Lorenz attractors through Šil'nikov-type bifurcation. Part IErgodic Theory and Dynamical Systems, 10
-
A. Rovella (1993)
The dynamics of perturbations of the contracting Lorenz attractorBoletim da Sociedade Brasileira de Matemática - Bulletin/Brazilian Mathematical Society, 24
-
V. Arnol’d (1994)
Dynamical Systems V -
M.J. Pacífico, A. Rovella (1993)
Unfolding contracting singular cyclesAnn. Scient. Ec. Norm. Sup. 4 Serie, T., 26
-
M. Pacifico, A. Rovella (1993)
Unfolding contracting singular cyclesAnnales Scientifiques De L Ecole Normale Superieure, 26
-
L.P. Sil'nikov (1966)
Generation of periodic motions from a trajectory exiting from an equilibrium of saddle-node and re-entering itSov. Math. Dokl., 7
-
R. Bamón, R. Labarca, R. Mãné, M. Pacifico (1993)
The explosion of singular cyclesPublications Mathématiques de l'Institut des Hautes Études Scientifiques, 78
-
L. Diaz (1995)
Persistence of cycles and nonhyperbolic dynamicsNonlinearity, 8
-
R. Labarca (1995)
Bifurcation of contracting singular cyclesAnn. Ec. Nor. Sup. T., 28
-
R. Labarca (1995)
Bifurcation of contracting singular cyclesAnnales Scientifiques De L Ecole Normale Superieure, 28
-
M.R. Richlik (1990)
Lorenz attractor through Sil'nikov-type bifurcation IErg. Th. and Dyn. Sys., 10
-
L. Díaz (1995)
Persistence of cycles and nonhyperbolic dynamics at heteroclinic bifurcationsNonlinearity, 8
-
R. Bamón, R. Labarca, R. Mañe, M.J. Pacífico (1993)
The explosion of singular cyclesPubl. Math. I.H.E.S., 78
- Publisher
- Springer Journals
- Copyright
- Copyright © 1999 by Sociedade Brasileira de Matemática
- Subject
- Mathematics; Mathematics, general; Theoretical, Mathematical and Computational Physics
- ISSN
- 1678-7544
- eISSN
- 1678-7714
- DOI
- 10.1007/BF01235870
- Publisher site
- See Article on Publisher Site
Abstract
At the boundary of the class of Morse-Smale vector fields there are vector fields whose unique degenerate phenomena is a singular cycle. We first characterize and classify all singular cycles which contains only one degeneracy (thesimple singular cycles: ssc). Each of these cycles defines a condimension one submanifold of vector fields. For some ssc its codimension one submanifold is a regular part of the boundary of the Morse-Smale systems. We characterize those ssc that defines this type of submanifold. Our ambient space isn dimensional,n≥2.
Journal
Bulletin of the Brazilian Mathematical Society, New Series – Springer Journals
Published: Feb 12, 2005