Cycles and bifurcation theory

Newhouse, S. ; Palis, J.

Trois études en dynamique qualitative, Astérisque, no. 31 (1976), 98 p.

MR 516408 | Zbl 0322.58009 | 3 citations dans Numdam

BibTeX
RIS

@incollection{AST_1976__31__43_0,
     author = {Newhouse, S. and Palis, J.},
     title = {Cycles and bifurcation theory},
     booktitle = {Trois \'etudes en dynamique qualitative},
     author = {Collectif},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {31},
     year = {1976},
     zbl = {0322.58009},
     mrnumber = {516408},
     language = {en},
     url = {http://www.numdam.org/item/AST_1976__31__43_0/}
}

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AU  - Newhouse, S.
AU  - Palis, J.
TI  - Cycles and bifurcation theory
BT  - Trois études en dynamique qualitative
AU  - Collectif
T3  - Astérisque
PY  - 1976
DA  - 1976///
IS  - 31
PB  - Société mathématique de France
UR  - http://www.numdam.org/item/AST_1976__31__43_0/
UR  - https://zbmath.org/?q=an%3A0322.58009
UR  - https://www.ams.org/mathscinet-getitem?mr=516408
LA  - en
ID  - AST_1976__31__43_0
ER  -

Newhouse, S.; Palis, J. Cycles and bifurcation theory, dans Trois études en dynamique qualitative, Astérisque, no. 31 (1976), 98 p. http://www.numdam.org/item/AST_1976__31__43_0/

Bibliographie
Cité par

[1] A. Andronov and R. Leontovich, I. I. Gordon, A. G. Maier, The theory of bifurcations of dynamical systems on the plane, "Nauka," Moscow, 1967. (Russian) MR 38 #3539. | MR 235228

[2] A. Andronov and L. Pontrjagin, Systemes grossiers, Dokl. Akad. Nauk. SSSR, vol. 14 (1937), 247-251. | JFM 63.0728.01 | Zbl 0016.11301

[3] P. Brunovsky, On one parameter families of diffeomorphisms, Comment. Math. Univ. Carolinae 11 (1970), 559-582. | EuDML 16385 | MR 279827 | Zbl 0202.23104

[4] J. Franks, Differentiably $Ω$ -stable diffeomorphisms, Topology 11 (1972), 107-114. | Article | MR 296972 | Zbl 0232.58006

[5] N. Gavrilov and L. Silnikov, On three dimensional dynamical systems close to systems with a structurally unstable homoclinic curve I, Math USSR Sbornik, Vol. 17 (1972), No. 4, 467-485. | Article | MR 310355 | Zbl 0255.58006

[6] J. Guckenheimer, Bifurcation and Catastrophe, Dynamical Systems, Ed. M. Peixoto, Academic Press, N. Y., 1973, 95-110. | MR 345139 | Zbl 0287.58005

[7] P. Hartman, Ordinary Differential Equations, J. Wiley and Sons, N. Y., 1964. | MR 171038 | Zbl 0125.32102

[8] M. Hirsch and C. Pugh, Stable manifolds and hyperbolic sets, Global Analysis, Proc. AMS Symp. in Pure Math., Vol. 14, 1970, 133-165. | Article | MR 271991 | Zbl 0215.53001

[9] M. Hirsch, C. Pugh, J. Palis, and M. Shub, Neighborhoods of hyperbolic sets, Invent. Math., Vol. 9 (1970), 121-134. | Article | EuDML 142000 | MR 262627 | Zbl 0191.21701

[10] M. Hirsch, C. Pugh, and M. Shub, Invariant manifolds, to appear. | MR 501173 | Zbl 0355.58009

[11] J. Moser, Stable and Random Motions in Dynamical Systems, Ann. of Math. Studies, No. 77, Princeton Univ. Press, Princeton, N. J., 1973. | MR 442980 | Zbl 0271.70009

[12] J. Moser, On a theorem of Anosov, Jour. Diff. Equations 5 (1969), 411-440. | Article | MR 238357 | Zbl 0169.42303

[13] J. Moser and C. Siegel, Lectures on Celestial Mechanics, Springer, Grundlehren Bd. 187, 1971. | MR 502448 | Zbl 0312.70017

[14] S. Newhouse, Non-density of Axiom $A (a)$ on $S^{2}$ , Global Analysis, Proc. AMS Symp in Pure Math, Vol. 14, 1970, 191-202. | MR 277005 | Zbl 0206.25801

[15] S. Newhouse, Hyperbolic limit sets, Trans. AMS 167 (1972), 125-150. | Article | MR 295388 | Zbl 0239.58009

[16] S. Newhouse, Diffeomorphisms with infinitely many sinks, Topology, Vol. 13 (1974), 9-18. | Article | MR 339291 | Zbl 0275.58016

[17] S. Newhouse, On simple arcs between structurally stable systems, to appear. | Zbl 0307.58011

[18] S. Newhouse and J. Palis, Bifurcations of Morse-Smale dynamical systems, Dynamical Systems, ed. M. Peixoto, Academic Press, N. Y., 1973, 303-366. | MR 334281 | Zbl 0279.58011

[19] S. Newhouse and M. Peixoto, There is a simple arc between any two Morse-Smale flows, to appear. | MR 516405 | Zbl 0324.58012

[20] J. Palis, On Morse-Smale dynamical systems, Topology 8 (1969), 385-405. | Article | MR 246316 | Zbl 0189.23902

[21] J. Palis, A note on $Ω$ -stability, Global Analysis, Proc. AMS Symp. in Pure Math., Vol. 14, Amer. Math. Soc., Providence, R. I., 1970, 221-222. | Article | MR 270387 | Zbl 0214.50801

[22] J. Palis and S. Smale, Structural stability theorems, Global Analysis, Proc. Symp. in Pure Math., Vol. 14, Amer. Math. Soc., Providence, R. I., 1970, 223-231. | Article | MR 267603 | Zbl 0214.50702

[23] M. Peixoto, Structural stability on two-dimensional manifolds, Topology 1 (1962), 101-120. | Article | MR 142859 | Zbl 0107.07103

[24] D. Ruelle and F. Takens, On the nature of turbulence, Comm. Math. Phys. 20 (1971), 167-192. | Article | MR 284067 | Zbl 0223.76041

[25] R. Sacker, On invariant surfaces and Bifurcation of periodic solutions of ordinary differential equations, New York University, IMM-NYU, 333, October, 1964. | MR 2615427 | Zbl 1173.37310

[26] M. Shub, Structurally stable systems are dense, Bull. A.M.S., Vol. 78 (1972), 817-818. | Article | MR 307278 | Zbl 0265.58003

[27] M. Shub, Dynamical Systems, filtrations, and entropy, Bull. A.M.S., to appear. | MR 334284 | Zbl 0305.58014

[28] M. Shub and D. Sullivan, Homology theory and dynamical systems, to appear. | MR 400306 | Zbl 0408.58023

[29] L. Silnikov, On a new type of bifurcation of multidimensional dynamical systems, Sov. Math. Dokl., Vol. 10 (1969), No. 6, 1368-1371. | Zbl 0219.34031

[30] S. Smale, On gradient dynamical systems, Ann. of Math. 74 (1961), 199-206. | Article | MR 133139 | Zbl 0136.43702

[31] S. Smale, Diffeomorphisms with many periodic points, Differential and Combinatorial Topology, Princeton Univ. Press, Princeton, N. J., 1965, 63-80. | MR 182020 | Zbl 0142.41103

[32] S. Smale, Differentiable dynamical systems, Bull. A.M.S. 73 (1967), 747-817. | Article | MR 228014 | Zbl 0202.55202

[33] S. Smale, The $Ω$ -stability theorem, Global Analysis, Proc. Symp. Pure Math. 14, Amer. Math. Soc., Providence, R. I., 1970, 289-298. | Article | MR 271971 | Zbl 0205.54104

[34] S. Smale, Stability and Isotopy in discrete dynamical systems, Dynamical Systems, ed. M. Peixoto, Academic Press, N. Y., 1973, 527-530. | MR 339222 | Zbl 0284.58013

[35] J. Sotomayor, Generic one parameter families of vector fields on two dimensional manifolds, Publ. Math. I.H.E.S., to appear. | EuDML 103932 | MR 339279 | Zbl 0279.58008

[36] J. Sotomayor, Generic bifurcations of Dynamical Systems, Dynamical Systems, ed. M. Peixoto, Academic Press, N. Y., 1973, 561-582. | MR 339280 | Zbl 0296.58007

[37] S. Sternberg, Local contractions and a theorem of Poincaré, Amer. J. Math. 79 (1957), 809-824. | Article | MR 96853 | Zbl 0080.29902

[38] S. Sternberg, On the structure of local homeomorphisms of Euclidean $n$ -space II, ibid 80 (1958), 623-631. | MR 96854 | Zbl 0083.31406

[39] F. Takens, Singularities of vector fields, to appear. | Article | MR 339292 | Zbl 0279.58009

[40] R. Thom, Stabilité Structurelle et Morphogénèse, Benjamin, N. Y. 1972. | MR 488155 | Zbl 0294.92001

[41] R. Williams, The "DA" maps of Smale and structural stability, Global Analysis, Proc. Symp. Pure Math. 14, Amer. Math. Soc., Providence, R. I., 1970, 329-335. | Article | MR 264705 | Zbl 0213.50303

[42] R. Williams, Classification of subshifts of finite type, Ann. of Math. 98 (1973), 120-153. | Article | MR 331436 | Zbl 0282.58008