journal article
Dec 01, 1988
Dimension formula for random transformations
Communications in Mathematical Physics
Vol. 117
No. 4
pp. 529-548
·
Springer Science and Business Media LLC
Topics
No keywords indexed for this article. Browse by subject →
References
18
[1]
Brin, M., Kifer, Y.: Dynamics of Markov chains and stable manifolds for random diffeomorphisms. Preprint
[2]
Brin, M., Nitecki, Z.: Absolute continuity of stable foliation in Hilbert space. In preparation
[3]
Carverhill, A.: Flows of stochastic dynamical systems: Ergodic theory. Stochastic14, 273?317 (1985)
10.1080/17442508508833343
[4]
Ergodic theory of chaos and strange attractors
J. -P. Eckmann, D. Ruelle
Reviews of Modern Physics
1985
10.1103/revmodphys.57.617
[5]
Frederickson, P., Kaplan, J. L., Yorke, E. D., Yorke, J. A.: The Lyapunov dimension of strange attractors. J. Differ. Equations49, 183?207 (1983)
10.1016/0022-0396(83)90011-6
[6]
Ikeda, N., Watanabe, S.: Stochastic differential equations and diffusion processes. Amsterdam: North-Holland Kodansha 1981
[7]
Kifer, Y.: Ergodic theory of Random Transformations. Progress in Probability and Statistics. Boston: Birkhäuser 1986
10.1007/978-1-4684-9175-3
[8]
Kifer, Y.: A note on integrability ofC r -norms of stochastic flows and applications, 1987 preprint
10.1007/bfb0077921
[9]
Katok, A., Strelcyn, J.-M.: Smooth maps with singularities; invariant manifolds, entropy and billiards. Lecture Notes in Math., Vol.1222, Berlin, Heidelberg, New York: Springer 1986
10.1007/bfb0099031
[10]
Kunita, H.: Stochastic differential equations and stochastic flow of diffeomorphisms. Ecole d'Eté de Probabilités de Saint-Flour XII. 1982; Hennequin, P.-L. (ed.). Lecture Notes in Math., Vol.1097. Berlin, Heidelberg, New York: Springer 1984
[11]
Le Jan, Y.: On isotropic Brownian motions. Z. Wahrscheinlichkeitstheorie Verw. Geb.70, 609?620 (1985)
10.1007/bf00531870
[12]
Ledrappier, F., Young, L.-S.: The metric entropy of diffeomorphisms, part II: Relations between entropy, exponents and dimension. Ann. Math.122, 540?574 (1985)
10.2307/1971329
[13]
Ledrappier, F., Young, L.-S.: Entropy formula for random transformations. Preprint.
[14]
Mañé, R.: On the dimension of the compact invariant sets of certain nonlinear maps. In: Dynamical systems and turbulence, Warwick, 1980. Lecture Notes in Mathematics, Vol.898. pp. 230?242 Berlin, Heidelberg, New York: Springer 1981
10.1007/bfb0091916
[15]
Marstrand, J. M.: Some fundamental geometrical properties of plane sets of fractional dimensions. Proc. Lond. Math. Soc.4, 257?302 (1954)
10.1112/plms/s3-4.1.257
[16]
Mattila, P.: Hausdorff Dimension, Orthogonal projections and Intersections with planes. Ann. Acad. Sci. Fennicae, Series A1 Math.1, 227?244 (1975)
10.5186/aasfm.1975.0110
[17]
Thieullen, P.: Fibrés dynamiques asymptotiquement compacts: Exposants de Lyapunov. Entropie. Dimension. Ann. Inst. Henri Poincaré Analyse non linéaire4, 49?97 (1987)
10.1016/s0294-1449(16)30373-0
[18]
Young, L.-S.: Dimension, entropy and Lyapunov exponents. Erg. Theory Dynam. Sys.2, 109?124 (1982)
10.1017/s0143385700009615
Metrics
68
Citations
18
References
Details
- Published
- Dec 01, 1988
- Vol/Issue
- 117(4)
- Pages
- 529-548
- License
- View
Authors
Cite This Article
F. Ledrappier, L. -S. Young (1988). Dimension formula for random transformations. Communications in Mathematical Physics, 117(4), 529-548. https://doi.org/10.1007/bf01218383
Related
You May Also Like
Intermittent transition to turbulence in dissipative dynamical systems
Yves Pomeau, PAUL MANNEVILLE · 1980
1,701 citations