Bifurcations and stability of families of diffeomorphisms
Publications Mathématiques de l'IHÉS, Volume 57 (1983), pp. 5-71.
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author = {Newhouse, Sheldon E. and Palis, Jacob and Takens, Floris},
title = {Bifurcations and stability of families of diffeomorphisms},
journal = {Publications Math\'ematiques de l'IH\'ES},
pages = {5--71},
publisher = {Institut des Hautes \'Etudes Scientifiques},
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year = {1983},
zbl = {0518.58031},
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url = {http://www.numdam.org/item/PMIHES_1983__57__5_0/}
}
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Newhouse, Sheldon E.; Palis, Jacob; Takens, Floris. Bifurcations and stability of families of diffeomorphisms. Publications Mathématiques de l'IHÉS, Volume 57 (1983), pp. 5-71. http://www.numdam.org/item/PMIHES_1983__57__5_0/

[1] A. A. Andronov, E. A. Leontovich, I. I. Gordon, A. G. Maier, Theory of bifurcations of dynamic systems on a plane, Isr. Program Scientific Transl., Jerusalem, 1971.

[2] L. Block, J. Franke, Existence of periodic points of maps of S1, Invent. Math., 22 (1973), 69-73. | EuDML | MR | Zbl

[3] Th. Bröcker, L. C. Lander, Differentiable germs and catastrophes, London Math. Soc. Lecture Notes, 17, Cambridge Univ. Press, 1975. | MR | Zbl

[4] P. Brunovski, On one-parameter families of diffeomorphisms, I and II, Comment. Mat. Univ. Carolinae, 11 (3) (1970), 559-582 ; 12 (4) (1971), 765-784. | EuDML | MR | Zbl

[5] P. Brunovski, Generic properties of the rotation number of one-parameter diffeomorphisms of the circle, Czech. Math. J., 24 (1974), 74-90. | EuDML | MR | Zbl

[6] A. Denjoy, Les trajectoires à la surface du tore, C. r. Acad. Sci., 223 (1946), 5-8. | MR | Zbl

[7] J. Guckenheimer, One-parameter families of vector fields on two-manifolds : another nondensity theorem, Dynamical Systems, Academic Press, 1973, 111-128. | MR | Zbl

[8] P. Hartman, On local homeomorphisms of Euclidean spaces, Bol. Soc. Mat. Mexicana, 5 (2) (1960), 220-241. | MR | Zbl

[9] M. Herman, Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations, Publ. Math. I.H.E.S., 49 (1979), 5-234. | EuDML | Numdam | MR | Zbl

[10] M. Herman, Mesure de Lebesgue et nombre de rotation, Geometry and Topology, Springer Lecture Notes in Math., 597 (1977), 271-293. | MR | Zbl

[11] M. W. Hirsch, C. C. Pugh, Stable manifolds and hyperbolic sets, Proc. Symp. Pure Math. A.M.S., 14 (1970), 133-164. | MR | Zbl

[12] M. W. Hirsch, C. C. Pugh, M. Shub, Invariant manifolds, Springer Lecture Notes in Math., 583 (1977). | MR | Zbl

[13] I. Kupka, Contributions à la théorie des champs génériques, Contributions to differential equations, vol. 2 (1963), 475-484 and vol. 3 (1964), 411-420. | MR | Zbl

[14] D. C. Lewis, Formal power series transformations, Duke Math. J., 5 (1939), 794-805. | JFM | MR | Zbl

[15] I. P. Malta, Hyperbolic Birkhoff centers, Trans. A.M.S., 262 (1980), 181-193 ; announced in An. Acad. Brasil. Ciências, 51 (1979), (I), 27-29. | Zbl

[16] A. Manning, There are no new Anosov diffeomorphisms on tori, Amer. J. Math., 96 (1974), 422-429. | MR | Zbl

[17] J. E. Marsden, M. Mccracken, The Hopf bifurcation and its applications, Appl. Math. Sci., 19, Springer-Verlag, 1976. | MR | Zbl

[18] W. C. De Melo, Moduli and stability of two-dimensional diffeomorphisms, Topology, 19 (1980), 9-21. | MR | Zbl

[18a] W. De Melo, J. Palis and S. Van Strien, Characterizing diffeomorphisms with modulus of stability one, Dynamical Systems and Turbulence, Warwick 1980, Springer Lecture Notes in Math., 898 (1981), 266-286. | Zbl

[19] S. Newhouse, J. Palis, Bifurcations of Morse-Smale dynamical systems, Dynamical Systems, Academic Press, 1973, 303-366. | MR | Zbl

[20] S. Newhouse, J. Palis, Cycles and bifurcation theory, Astérisque, 31 (1976), 43-140. | MR | Zbl

[21] S. Newhouse, J. Palis, F. Takens, Stable arcs of diffeomorphisms, Bull. A.M.S., 82 (1976), 499-502. | MR | Zbl

[22] S. Newhouse, The abundance of wild hyperbolic sets and non-smooth stable sets, Publ. Math. I.H.E.S., 50 (1979), 101-152. | Numdam | MR | Zbl

[23] R. Palais, Local triviality of the restriction map for embeddings, Comm. Math. Helvet., 34 (1960), 305-312. | MR | Zbl

[24] J. Palis, On Morse-Smale dynamical systems, Topology, 8 (1969), 385-405. | MR | Zbl

[25] J. Palis, S. Smale, Structural stability theorems, Proc. Symp. Pure Math. A.M.S., 14 (1970), 223-232. | MR | Zbl

[26] J. Palis, F. Takens, Topological equivalence of normally hyperbolic dynamical systems, Topology, 16 (1977), 335-345. | MR | Zbl

[26a] J. Palis and F. Takens, Stability of parametrized families of gradient vector fields, Preprint IMPA, to appear. | Zbl

[27] J. Palis, A differentiable invariant of topological conjugacies and moduli of stability, Astérisque, 51 (1978), 335-346. | MR | Zbl

[28] J. Palis, Moduli of stability and bifurcation theory, Proc. Int. Congres of Math. Helsinki (1978), 835-839. | MR | Zbl

[29] H. Poincaré, Œuvres complètes, t. 1, Gauthier-Villars, 1952, 137-158.

[30] C. C. Pugh, M. Shub, Linearization of normally hyperbolic diffeomorphisms and flows, Invent. Math., 10 (1970), 187-198. | MR | Zbl

[31] C. Robinson, Global structural stability of a saddle-node bifurcation, Trans. A.M.S., 236 (1978), 155-172. | MR | Zbl

[32] D. Ruelle, F. Takens, On the nature of turbulence, Comm. Math. Phys., 20 (1971), 167-192 ; A note concerning our paper on the nature of turbulence, Comm. Math. Phys., 23 (1971), 343-344. | MR | Zbl

[33] S. Smale, Stable manifolds for differential equations and diffeomorphisms, Ann. Scuola Norm. Sup. Pisa, 18 (1963), 97-116. | Numdam | MR | Zbl

[34] S. Smale, Differentiable dynamical systems, Bull. A.M.S., 73 (1967), 747-817. | MR | Zbl

[35] J. Sotomayor, Generic one parameter families of vector fields, Publ. Math. I.H.E.S., 43 (1974), 4-56. | Numdam | Zbl

[36] J. Sotomayor, Generic bifurcations of dynamical systems, Dynamical Systems, Academic Press 1973, 549-560.

[37] S. J. Van Strien, Center manifolds are not C∞, Math. Z., 166 (1979), 143-145. | MR | Zbl

[38] F. Takens, Partially hyperbolic fixed points, Topology, 10 (1971), 133-147. | MR | Zbl

[39] F. Takens, Normal forms for certain singularities of vector fields, Ann. Inst. Fourier, 23 (1973), (2), 163-195. | Numdam | MR | Zbl

[40] F. Takens, Forced oscillations and bifurcations, Applications of Global Analysis I, Comm. of the Math. Inst., R.U. Utrecht (Holland), 1974. | MR | Zbl

[41] F. Takens, Global phenomena in bifurcations of dynamical systems with simple recurrence, Jber. d. Dt. Math.-Verein, 81 (1979), 87-96. | MR | Zbl

[42] R. Williams, The D.A. map of Smale and structural stability, Proc. Symp. Pure Math. A.M.S., 14 (1970), 329-334. | MR | Zbl