Global stability of saddle-node bifurcation of a periodic orbit for vector fields

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1. [1] De Melo ( W.), Palis ( J.) and Van Strien ( S.) .— Caracterising diffeomorphisms with modulus of stability one, Lectures Notes in Math.898 (1981), pp. 226-285. Zbl0482.58022
2. [2] De Melo ( W.) and Palis ( J.) .— Moduli of stability for diffeomorphisms, Lectures Notes in Math.819 (1980), pp. 315-339. Zbl0445.58020MR591192
3. [3] Hirsch ( M.), Pugh ( C.) and Shub ( M.) .— Invariant Manifolds, Lectures Notes in Math., Springer Verlag, 583 (1977). Zbl0355.58009MR501173
4. [4] Labarca ( R.) .— Stability of parametrized families of vector fields, Dynamical Systems and Bifurcations Theory, Eds M. I. Camacho, M. J. Pacífico & F. Takens, Pitman Research Notes in Math., Serie 160 (1987), pp. 121-213. Zbl0632.58026
5. [5] Labarca ( R.) and Pacífico ( M.J.) .— Stability of Morse-Smale vector fields on n-manifolds with boundary, Preprint U.F.R.J., Brazil (1988). MR1046625
6. [6] Malta ( I.P.) and Palis ( J.) .— Families of Vector fields with finite modulus of Stability, Lectures Notes in Math.898 (1980), pp. 212-229. Zbl0482.58023MR654891
7. [7] Moeckel ( R.) .— Spiralling invariant manifold, J. Diff. Eq.66 (1987), pp. 189-207. Zbl0634.58016MR871994
8. [8] Newhouse ( S.), Palis ( J.) and Takens ( F.) .— Bifurcation and Stability of Families of Diffeomorphisms, Publ. Math. I.H.E.S.57 (1983), pp. 5-71. Zbl0518.58031MR699057
9. [9] Palis ( J.) and Takens ( F.) .— Stability of Parametrized families of gradient vector fields, Annals of Math.118 (1983), pp. 383-421. Zbl0533.58018MR727698
10. [10] Takens ( F.) . — Moduli and Bifurcations, non- transversal intersections of invariant manifold of vector fields, Lectures Notes in Math.799 (1980), pp. 368-384. Zbl0473.58018MR585498
11. [11] Takens ( F.) .— Global phenomena in bifurcations of dynamical systems with simple recurrence, Jber. der. Dentsche Math. Verein 81 (1979), pp. 81-96. Zbl0419.58012MR535099
12. [12] Takens ( F.) .— Normal Forms for Certain Singularities of Vector Fields, Ann. Inst. Fourier23, n° 2 (1973), pp. 163-195. Zbl0266.34046MR365620
13. [13] Van Strien ( S.) .— One parameter families of vector fields. Bifurcations near saddle connection, Ph. D. Thesis, Utrecht (1982). 

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