Ergodic theory of differentiable dynamical systems

David Ruelle

Publications Mathématiques de l'IHÉS (1979)

  • Volume: 50, page 27-58
  • ISSN: 0073-8301

How to cite

top

Ruelle, David. "Ergodic theory of differentiable dynamical systems." Publications Mathématiques de l'IHÉS 50 (1979): 27-58. <http://eudml.org/doc/103964>.

@article{Ruelle1979,
author = {Ruelle, David},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {multiplicative ergodic theorem; existence of stable manifolds; subadditive ergodic theorem; diffeomorphisms of class C(1+epsilon)},
language = {eng},
pages = {27-58},
publisher = {Institut des Hautes Études Scientifiques},
title = {Ergodic theory of differentiable dynamical systems},
url = {http://eudml.org/doc/103964},
volume = {50},
year = {1979},
}

TY - JOUR
AU - Ruelle, David
TI - Ergodic theory of differentiable dynamical systems
JO - Publications Mathématiques de l'IHÉS
PY - 1979
PB - Institut des Hautes Études Scientifiques
VL - 50
SP - 27
EP - 58
LA - eng
KW - multiplicative ergodic theorem; existence of stable manifolds; subadditive ergodic theorem; diffeomorphisms of class C(1+epsilon)
UR - http://eudml.org/doc/103964
ER -

References

top
  1. [1] M. A. AKCOGLU and L. SUCHESTON, A ratio ergodic theorem for superadditive processes, to appear. Zbl0386.60045
  2. [2] R. BOWEN and D. RUELLE, The ergodic theory of Axiom A flows, Inventiones math., 29 (1975), 181-202. Zbl0311.58010MR52 #1786
  3. [3] Y. DERRIENNIC, Sur le théorème ergodique sous-additif, C.R.A.S. Paris, 281 A (1975), 985-988. Zbl0327.60028MR53 #763
  4. [4] H. FURSTENBERG and H. KESTEN, Products of random matrices, Ann. Math. Statist., 31 (1960), 457-469. Zbl0137.35501MR22 #12558
  5. [5] M. W. HIRSCH, Differential topology, Graduate Texts in Mathematics, n° 33, Berlin, Springer, 1976. Zbl0356.57001MR56 #6669
  6. [6] M. HIRSCH, C. PUGH and M. SHUB, Invariant manifolds, Lecture Notes in Math., n° 583, Berlin, Springer, 1977. Zbl0355.58009MR58 #18595
  7. [7] K. JACOBS, Lecture notes on ergodic theory (2 vol.), Aarhus, Aarhus Universitet, 1963. Zbl0196.31301
  8. [8] S. KATOK, The estimation from above for the topological entropy of a diffeomorphism, to appear. Zbl0448.58010
  9. [9] J. F. C. KINGMAN, The ergodic theory of subadditive stochastic processes, J. Royal Statist. Soc., B 30 (1968), 499-510. Zbl0182.22802MR40 #8114
  10. [10] J. F. C. KINGMAN, Subadditive processes, in École d'été des probabilités de Saint-Flour, Lecture Notes in Math., n° 539, Berlin, Springer, 1976. Zbl0367.60030MR55 #11388
  11. [11] V. I. OSELEDEC, A multiplicative ergodic theorem. Ljapunov characteristic numbers for dynamical systems, Trudy Moskov. Mat. Obšč, 19 (1968), 179-210. English transl. Trans. Moscow Math. Soc., 19 (1968), 197-231. Zbl0236.93034
  12. [12] Ya. B. PESIN, Lyapunov characteristic exponents and ergodic properties of smooth dynamical systems with an invariant measure, Dokl. Akad. Nauk SSSR, 226, n° 4 (1976), 774-777. English transl. Soviet Math. Dokl., 17, n° 1 (1976), 196-199. Zbl0345.58010
  13. [13] Ya. B. PESIN, Invariant manifold families which correspond to nonvanishing characteristic exponents, Izv. Akad. Nauk SSSR, Ser. Mat. 40, n° 6 (1976), 1332-1379. English transl. Math. USSR Izvestija, 10, n° 6 (1976), 1261-1305. Zbl0383.58012
  14. [14] Ya. B. PESIN, Lyapunov characteristic exponents and smooth ergodic theory, Uspehi Mat. Nauk, 32, n° 4 (196) (1977), 55-112. English transl., Russian Math. Surveys, 32, n° 4 (1977), 55-114. Zbl0383.58011
  15. [15] M. S. RAGHUNATHAN, A proof of Oseledec' multiplicative ergodic theorem. Israel. J. Math., to appear. Zbl0415.28013
  16. [16] D. RUELLE, A measure associated with axiom A attractors, Amer. J. Math., 98 (1976), 619-654. Zbl0355.58010MR54 #3763
  17. [17] D. RUELLE, An inequality for the entropy of differentiable maps, Bol. Soc. Bras. Mat., 9 (1978), 83-87. Zbl0432.58013MR80f:58026
  18. [18] D. RUELLE, Sensitive dependence on initial condition and turbulent behavior of dynamical systems, Ann. N.Y. Acad. Sci., to appear. Zbl0438.58003
  19. [19] Ya. G. SINAI, Gibbs measures in ergodic theory, Uspehi Mat. Nauk, 27, n° 4 (1972), 21-64. English transl. Russian Math. Surveys, 27, n° 4 (1972), 21-69. Zbl0255.28016MR53 #3265
  20. [20] S. SMALE, Notes on differentiable dynamical systems, Proc. Sympos. Pure Math., 14, A.M.S., Providence, R.I. (1970), pp. 277-287. Zbl0205.54201MR42 #1152
  21. [21] J. TITS, Travaux de Margulis sur les sous-groupes discrets de groupes de Lie, Séminaire Bourbaki, exposé n° 482 (1976), Lecture Notes in Math., n° 567, Berlin, Springer, 1977. Zbl0346.22011
  22. [22] A. WEIL, Basic number theory, Berlin, Springer, 1973, 2nd ed. Zbl0267.12001

Citations in EuDML Documents

top
  1. Anatole Katok, Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
  2. François Ledrappier, Propriétés ergodiques des mesures de Sinaï
  3. Maciej Wojtkowski, Hamiltonian systems with linear potential and elastic constraints
  4. Viktor Aleksandrovich Pliss, О гиперболичности гладких коциклов над потоками с инвариантной эргодической мерой
  5. David Ruelle, Rotation numbers for diffeomorphisms and flows
  6. S. Siboni, Lyapunov exponents, KS-entropy and correlation decay in skew product extensions of Bernoulli endomorphisms
  7. Charles C. Pugh, The C 1 + α hypothesis in Pesin theory
  8. Albert Raugi, Théorème ergodique multiplicatif. Produits de matrices aléatoires indépendantes
  9. Sophie Lemaire, Invariant jets of a smooth dynamical system
  10. Paulo R. C. Ruffino, Luiz A. B. San Martin, Lyapunov exponents for stochastic differential equations on semi-simple Lie groups

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.