Mathematical theory of Lyapunov exponents

Journal of Physics A: Mathematical and Theoretical

Volumn 46, Issue 25, 2013, Pages

  Young, Lai Sang ^a  

^a NEW YORK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84878799013     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/46/25/254001     Document Type: Review

References (52)

1. Anosov D 1969 Geodesic Flows on Closed Riemann Manifolds With Negative Curvature (Providence, RI: American Mathematical Society) pp 1-235
2. Arnold L 2003 Random Dynamical Systems (Springer Monographs in Mathematics) (Berlin: Springer)
3. Benedicks M and Carleson L 1991 The dynamics of the Hénon map Ann. Math. 133 73-169
4. Benedicks M and Young L-S 1993 Sinai-Bowen-Ruell measure for certain Hénon maps Invent. Math. 112 541-76
5. Bowen R 1975 Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms (Lecture Notes in Mathematics vol 470) (Berlin: Springer)
6. Bowen R and Ruelle D 1975 The ergodic theory of Axiom A flows Invent. Math. 29 181-202
7. Demers M, Wright P and Young L-S 2012 Entropy, Lyapunov exponents and escape rates in open systems Ergodic Theory Dyn. Syst. 32 1270-301
8. Duarte P 1994 Plenty of elliptic islands for the standard family of area preserving maps Ann. Inst. H Poincaré C 11 359-409
9. Eckmann J P and Ruelle D 1985 Ergodic theory of chaos and strange attractors Rev. Mod. Phys. 57 617-56
10. Frederickson P, Kaplan J L, Yorke E D and Yorke J A 1983 The Lyapunov dimension of strange attractors J. Differ. Eqns 49 183-207
11. Gorodetski A 2012 On stochastic sea of the standard map Commun. Math. Phys. 309 155-92
12. Graczyk J and Swiatek G 1997 Generic hyperbolicity in the logistic family Ann. Math. 146 1-52
13. Hu H and Young L-S 1995 Nonexistence of SBR measures for some diffeomorphisms that are 'almost Anosov' Ergodic Theory Dyn. Syst. 15 67-76
14. Jakobson M 1981 Absolutely continues invariant measures for one-parameter families of one-dimensional maps Commun. Math. Phys. 81 39-88
15. Kifer Y 1974 On small random perturbations of some smooth dynamical systems Math. USSR Ivestija 8 1083-107
16. Kifer Y 1986 Ergodic Theory of Random Transformations (Progress in Probability and Statistics) (Basel: Birkhäuser)
17. Kunita H 1990 Stochastic Flows and Stochastic Differential Equations (Cambridge: Cambridge University Press)
18. Ledrappier F and Strelcyn J-M 1982 A proof of the estimation from below in Pesin entropy formula Ergodic Theory Dyn. Syst. 2 203-19
19. Ledrappier F 1984 Propriétés ergodiques des mesures de Sinai Inst. Hautes Etud. Sci. Publ. Math. 59 163-88
20. Ledrappier F and Young L-S 1985 The metric entropy of diffeomorphisms Part I Ann. Math. 122 509-39
21. Ledrappier F and Young L-S 1985 The metric entropy of diffeomorphisms Part II Ann. Math. 122 540-74
22. Ledrappier F and Young L-S 1988 Entropy formula for random transformations Prob. Theory Relat. Fields 80 217-40
23. Ledrappier F and Young L-S 1988 Dimension formula for random transformations Commun. Math. Phys. 117 529-48
24. Jan Y L 1987 Équilibre statistique pour les produits de diffeomorphismes aléatoires indépendants Ann. Inst. H Poincaré B 23 111-20
25. Lin K, Shea-Brown E and Young L-S 2009 Reliability of coupled oscillators J. Nonlinear Sci. 19 497-545
26. Lin K and Young L-S 2010 Dynamics of periodically-kicked oscillators J. Fixed Point Theory Appl. 7 291-312
27. Liverani C and Wojtkowski M 1995 Ergodicity in Hamiltonian systems Dyn. Rep. 4 130-202
28. Lu K, Wang Q D and Young L-S 2013 Strange attractors for periodically forced parabolic equations Mem. Am. Math. Soc. at press
29. Lyubich M 1997 Dynamics of quadratic polynomials: I and II Acta Math. 178 185-297
30. Lyubich M 2002 Almost every real quadratic map is either regular or stochastic Ann. Math. 156 1-78
31. Newhouse S 1980 Lectures on Dynamical Systems (Progress in Mathematics vol 8) (Basel: Birkhäuser) pp 1-114
32. Oseledec V I 1968 A multiplicative ergodic theorem: Lyapunov characteristic numbers of dynamical systems Trans. Moscow Math. Soc. 19 197-231
33. Pesin Y B 1977 Characteristic Lyapunov exponents and smooth ergodic theory Russ. Math. Surv. 32 55-114
34. Pesin Y B and Sinai Y G 1982 Gibbs measures for partially hyperbolic attractors Ergodic Theory Dyn. Syst. 2 417-38
35. Pugh C and Shub M 1989 Ergodic attractors Trans. Am. Math. Soc. 312 1-54
36. Pugh C and Shub M 2000 Stable ergodicity and Julienne quasi-conformality J. Eur. Math. Soc. 2 1-52
37. Pugh C, Shub M and Starkov A 2004 Corrigendum: Stable ergodicity and Julienne quasi-conformality J. Eur. Math. Soc. 6 149-51 (corrigendum)
38. Ruelle D 1976 A measure associated with Axiom A attractors Am. J. Math. 98 619-54
39. Ruelle D 1979 Ergodic theory of differentiable dynamical systems Publ. Math. IHES 50 27-58
40. Ruelle D 1978 An inequality of the entropy of differentiable maps Bol. Soc. Bras. Mat. 9 83-7
41. Sinai Y G 1970 Dynamical systems with elastic reflections: ergodic properties of dispersing billiards Russ. Math. Surv. 25 137-89
42. Sinai Ya G 1972 Gibbs measures in ergodic theory Russ. Math. Surv. 27 21-69
43. Smale S 1967 Differentiable dynamical systems Bull. Am. Math. Soc. 73 747-817
44. Walters P 1982 An Introduction to Ergodic Theory (Graduate Texts in Mathematics) (Berlin: Springer)
45. Wang Q and Young L-S 2001 Strange attractors with one direction of instability Commun. Math. Phys. 218 1-97
46. Wang Q and Young L-S 2002 From invariant curves to strange attractors Commun. Math. Phys. 225 275-304 (Pubitemid 40830985)
47. Wang Q and Young L-S 2008 Toward a theory of rank-1 attractors Ann. Math. 167 349-480
48. Wojtkowski M 1985 Invariant families of cones and Lyapunov exponents Ergodic Theory Dyn. Syst. 5 145-61
49. Wojtkowski M 1986 Principles for the design of billiards with nonvanishing Lyapunov exponents Commun. Math. Phys. 105 391-414
50. Young L-S 1985 Bowen-Ruelle measures for certain piecewise hyperbolic maps Trans. Am. Math. Soc. 287 41-8
51. Young L-S 1986 Stochastic stability of hyperbolic attractors Ergodic Theory Dyn. Syst. 6 311-9
52. Young L-S 1990 Some large deviation results for dynamical systems Trans. Am. Math. Soc. 318 525-43