Local and Global Lyapunov exponents

Springer Science and Business Media LLC - Tập 3 Số 1 - Trang 133-177 - 1991
A. Eden1, Ciprian Foiaş2, Roger Témam3
1Department of Mathematics, Swain East No. 222, Indiana University, 47405, Bloomington, Indiana
2Department of Mathematics, Swain East No. 310, and The Institute for Applied Mathematics & Scientific Computing, Indiana University, 618 East 3rd Street, 47405, Bloomington, Indiana
3Laboratoire d'Analyse Numérique, Bat. 425, Université Paris-Sud, 91405, Orsay, France

Tóm tắt

Từ khóa


Tài liệu tham khảo

Constantin, P., and Foias, C. (1985). Global Lyapunov exponents, Kaplan-Yorke formulas and the dimension of the attractors for 2D Navier-Stokes equations.Comm. Pure Appl. Math. 38, 1?27.

Constantin, P., Foias, C., and Temam, R. (1985).Attractors Representing Turbulent Flows, AMS Memoirs, Vol. 53, No. 314.

Constantin, P., Foias, C., Nicolaenko, B., and Temam, R. (1988).Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations, Applied Mathematical Sciences Vol. 70, Springer-Verlag, New York.

Choquet, G., and Foias, C. (1975). Solution d'un problème sur les itérés d'un opérateur positif sur ?(k) et propriétés de moyennes associées.Ann. Inst. Fourier Grenoble 25, 109?129.

Douady, A., and Osterle, J. (1980). Dimension de Hausdorff des attracteurs.C.R. Acad. Sci. Paris 290 (Ser. A), 1135?1138.

Farmer, J. D. (1982). Chaotic attractors of an infinite dimensional dynamical systems.Physica 4D, 366?393.

Kaplan, J., and Yorke, J. (1979). Chaotic behaviour of multidimensional difference equations.Functional Difference Equations and Approximation of Fixed Points, Lecture Notes in Mathematics 730, Springer-Verlag, Berlin.

Kolmogorov, A. N., and Tihomirov, V. M. (1959).?-entropy and?-capacity of sets in functional spaces.Uspehi Mat. Nauk 14, 3?86.

Ledrappier, F. (1981). Some relations between dimension and Lyapunov exponents.Comm. Math. Phys. 81, 223?238.

Rogers, C. A. (1970).Hausdorff Measure, Cambridge University Press, Cambridge.

Ruelle, D. (1979). Ergodic theory of differential dynamical systems.Publ. Mathe. IHES 50, 275?306.

Temam, R. (1988).Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Applied Mathematical Sciences Vol. 68, Springer-Verlag, New York.

Walters, P. (1982).An Introduction to Ergodic Theory, Springer-Verlag, New York.

Yomdin, G. (1986). Volume growth and entropy. Preprint.