@article{PMIHES_1983__57__5_0, 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}, volume = {57}, year = {1983}, mrnumber = {84g:58080}, zbl = {0518.58031}, language = {en}, url = {http://www.numdam.org/item/PMIHES_1983__57__5_0/} }
TY - JOUR AU - Newhouse, Sheldon E. AU - Palis, Jacob AU - Takens, Floris TI - Bifurcations and stability of families of diffeomorphisms JO - Publications Mathématiques de l'IHÉS PY - 1983 SP - 5 EP - 71 VL - 57 PB - Institut des Hautes Études Scientifiques UR - http://www.numdam.org/item/PMIHES_1983__57__5_0/ LA - en ID - PMIHES_1983__57__5_0 ER -
%0 Journal Article %A Newhouse, Sheldon E. %A Palis, Jacob %A Takens, Floris %T Bifurcations and stability of families of diffeomorphisms %J Publications Mathématiques de l'IHÉS %D 1983 %P 5-71 %V 57 %I Institut des Hautes Études Scientifiques %U http://www.numdam.org/item/PMIHES_1983__57__5_0/ %G en %F PMIHES_1983__57__5_0
Newhouse, Sheldon E.; Palis, Jacob; Takens, Floris. Bifurcations and stability of families of diffeomorphisms. Publications Mathématiques de l'IHÉS, Tome 57 (1983), pp. 5-71. http://www.numdam.org/item/PMIHES_1983__57__5_0/
[1] Theory of bifurcations of dynamic systems on a plane, Isr. Program Scientific Transl., Jerusalem, 1971.
, , , ,[2] Existence of periodic points of maps of S1, Invent. Math., 22 (1973), 69-73. | EuDML | MR | Zbl
, ,[3] Differentiable germs and catastrophes, London Math. Soc. Lecture Notes, 17, Cambridge Univ. Press, 1975. | MR | Zbl
, ,[4] 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] Generic properties of the rotation number of one-parameter diffeomorphisms of the circle, Czech. Math. J., 24 (1974), 74-90. | EuDML | MR | Zbl
,[6] Les trajectoires à la surface du tore, C. r. Acad. Sci., 223 (1946), 5-8. | MR | Zbl
,[7] One-parameter families of vector fields on two-manifolds : another nondensity theorem, Dynamical Systems, Academic Press, 1973, 111-128. | MR | Zbl
,[8] On local homeomorphisms of Euclidean spaces, Bol. Soc. Mat. Mexicana, 5 (2) (1960), 220-241. | MR | Zbl
,[9] 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] Mesure de Lebesgue et nombre de rotation, Geometry and Topology, Springer Lecture Notes in Math., 597 (1977), 271-293. | MR | Zbl
,[11] Stable manifolds and hyperbolic sets, Proc. Symp. Pure Math. A.M.S., 14 (1970), 133-164. | MR | Zbl
, ,[12] Invariant manifolds, Springer Lecture Notes in Math., 583 (1977). | MR | Zbl
, , ,[13] 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] Formal power series transformations, Duke Math. J., 5 (1939), 794-805. | JFM | MR | Zbl
,[15] Hyperbolic Birkhoff centers, Trans. A.M.S., 262 (1980), 181-193 ; announced in An. Acad. Brasil. Ciências, 51 (1979), (I), 27-29. | Zbl
,[16] There are no new Anosov diffeomorphisms on tori, Amer. J. Math., 96 (1974), 422-429. | MR | Zbl
,[17] The Hopf bifurcation and its applications, Appl. Math. Sci., 19, Springer-Verlag, 1976. | MR | Zbl
, ,[18] Moduli and stability of two-dimensional diffeomorphisms, Topology, 19 (1980), 9-21. | MR | Zbl
,[18a] Characterizing diffeomorphisms with modulus of stability one, Dynamical Systems and Turbulence, Warwick 1980, Springer Lecture Notes in Math., 898 (1981), 266-286. | Zbl
, and ,[19] Bifurcations of Morse-Smale dynamical systems, Dynamical Systems, Academic Press, 1973, 303-366. | MR | Zbl
, ,[20] Cycles and bifurcation theory, Astérisque, 31 (1976), 43-140. | Numdam | MR | Zbl
, ,[21] Stable arcs of diffeomorphisms, Bull. A.M.S., 82 (1976), 499-502. | MR | Zbl
, , ,[22] 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] Local triviality of the restriction map for embeddings, Comm. Math. Helvet., 34 (1960), 305-312. | MR | Zbl
,[24] On Morse-Smale dynamical systems, Topology, 8 (1969), 385-405. | MR | Zbl
,[25] Structural stability theorems, Proc. Symp. Pure Math. A.M.S., 14 (1970), 223-232. | MR | Zbl
, ,[26] Topological equivalence of normally hyperbolic dynamical systems, Topology, 16 (1977), 335-345. | MR | Zbl
, ,[26a] Stability of parametrized families of gradient vector fields, Preprint IMPA, to appear. | Zbl
and ,[27] A differentiable invariant of topological conjugacies and moduli of stability, Astérisque, 51 (1978), 335-346. | Numdam | MR | Zbl
,[28] Moduli of stability and bifurcation theory, Proc. Int. Congres of Math. Helsinki (1978), 835-839. | MR | Zbl
,[29] Œuvres complètes, t. 1, Gauthier-Villars, 1952, 137-158.
,[30] Linearization of normally hyperbolic diffeomorphisms and flows, Invent. Math., 10 (1970), 187-198. | MR | Zbl
, ,[31] Global structural stability of a saddle-node bifurcation, Trans. A.M.S., 236 (1978), 155-172. | MR | Zbl
,[32] 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] Stable manifolds for differential equations and diffeomorphisms, Ann. Scuola Norm. Sup. Pisa, 18 (1963), 97-116. | Numdam | MR | Zbl
,[34] Differentiable dynamical systems, Bull. A.M.S., 73 (1967), 747-817. | MR | Zbl
,[35] Generic one parameter families of vector fields, Publ. Math. I.H.E.S., 43 (1974), 4-56. | Numdam | Zbl
,[36] Generic bifurcations of dynamical systems, Dynamical Systems, Academic Press 1973, 549-560.
,[37] Center manifolds are not C∞, Math. Z., 166 (1979), 143-145. | MR | Zbl
,[38] Partially hyperbolic fixed points, Topology, 10 (1971), 133-147. | MR | Zbl
,[39] Normal forms for certain singularities of vector fields, Ann. Inst. Fourier, 23 (1973), (2), 163-195. | Numdam | MR | Zbl
,[40] Forced oscillations and bifurcations, Applications of Global Analysis I, Comm. of the Math. Inst., R.U. Utrecht (Holland), 1974. | MR | Zbl
,[41] Global phenomena in bifurcations of dynamical systems with simple recurrence, Jber. d. Dt. Math.-Verein, 81 (1979), 87-96. | MR | Zbl
,[42] The D.A. map of Smale and structural stability, Proc. Symp. Pure Math. A.M.S., 14 (1970), 329-334. | MR | Zbl
,