References
References
- Abate M An introduction to Hyperbolic Dynamical Systems Universitá di Pisa, Dipartimento di Matematica
- Abbondandolo A Majer P 2001 On the Stable Manifold Theorem (Preprint)
- Benedicks , M and Carleson , L . 1991 . The dynamics of the Heńon map . Ann. of Mathe. , 133 : 73 – 169 .
- Chaperon M 2001 Some results on stable manifolds Comptes Rendus de l'Académie des Sciences, Paris. Série I. Mathématique 333 119 124 1 847 357 (English, with English and French summaries)
- Chaperon M 2002 Invariant manifolds revisited Trudy Mathematicheskogo Instituta Imeni VA Steklova 236 428 446 Dedicated to the 80th annniversary of Academician Evgeniî Frolovich Mishchenko (Russian) (Suzdal, 2000). 1 931 043
- Fathi A Herman M Yoccoz J-C 1983 A proof of Pesin's stable manifold theorem Geometric Dynamics (Rio de Janeiro 1981), Lect. Notes in Math. Berlin Springer Verlag vol. 1007 177 215
- Fenichel , N . 1971 . Persistence and smoothness of invariant manifolds of flows . Indiana University Mathematics Journal , 21 : 193 – 226 .
- — . 1974 . Asymptotic stability with rate conditions . Indiana University Mathematics Journal , 23 : 1109 – 1137 .
- — . 1977 . Asymptotic stability with rate conditions, II . Indiana University Mathematics Journal , 26 : 81 – 93 .
- Hadamard , J . 1901 . Sur l'iteration it les solutions asymptotetiques des equations differentielles . Bulletin de la Socété Matématique de France , 29 : 224 – 228 .
- Hirsch M Pugh C Shub M 1977 Invariant Manifolds Lecture Notes in Math. Springer vol. 583
- Holland MP Luzzatto S 2004 (In progress) Stable Manifolds under Very Weak Hyperbolicity Conditions
- Irwin , MC . 1970 . On the stable manifold theorem . Bulletin of the London Mathematical Society , 2 : 196 – 198 .
- Kan , I . 1994 . Open sets of diffeomorphisms having two attractors, each with an everywhere dense basin . Bulletin of the American Mathematical Society , 31 : 68 – 74 .
- Katok A Hasselblatt B 1994 Introduction to the Modern Theory of Smooth Dynamical Systems
- Luzzatto S Viana M 2003 Lorenz-like Attractors Without Continuous Invariant Foliations (Preprint)
- Mora L Viana M 1993 Abundance of strange attractors Acta Mathematica 171 1 71 MR 94k:58089
- Moser J 1973 Stable and Random Motions in Dynamical Systems, Priceton University Press
- Palis J Takens F 1993 Hyperbolicity and Sensitive-chaotic Dynamics at Homoclinic Bifurcations, Cambridge University Press: Cambridge
- Pesin , Ya. 1976 . Families of invariant manifolds corresponding to non-zero characteristic exponents . Mathematics of the USSR Izvestija , 10 : 1261 – 1302 .
- Pesin , Ya. B . 1977 . Characteristic Lyapunov exponents and smooth ergodic theory . Russian Mathematical Surveys , 324 : 55 – 114 .
- Poincaré , H . 1890 . Sur le problème des trois corps et les équations de la dynamique . Acta Mathematica , 13 : 1 – 270 .
- Robinson C 1995 Dynamical Systems, CRC Press
- Ruelle D Shub M 1980 Stable manifolds for maps Global Theory of Dynamical Systems, Lect. Notes in Math. Springer Verlag vol. 819 389 392
- Smale , S . 1963 . Stable manifolds for differential equations and diffeomorphisms . Annali della Scuola Normale Superiore di Pisa , 18 : 97 – 116 .
- Wang Q Young L-S 2001 Strange attractors with one direction of instability Communications in Mathematical Physics 218 1 97 MR 2002m:37050
- Wiggins S 1994 Normally Hyperbolic Invariant Manifolds in Dynamical Systems New York, Berlin, Heidelberg Springer-Verlag