Nonremovable zero Lyapunov exponent

Functional Analysis and its Applications

Volumn 39, Issue 1, 2005, Pages 21-30

  Gorodetski, A S ^a,b   Ilyashenko, Yu S ^a,c,d,e   Kleptsyn, V A ^a,c,f   Nalsky, M B ^c  

^a INDEPENDENT UNIVERSITY OF MOSCOW   (Russian Federation)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^c MOSCOW STATE UNIVERSITY   (Russian Federation)

^d Cornell University ^*  (United States)

^e STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

^f UNITÉ DE MATHÉMATIQUES PURES ET APPLIQUÉES   (France)

Author keywords

Bernoulli diffeomorphism; Dynamical system; Lyapunov exponent; Nonuniform hyperbolicity; Partially hyperbolic system; Skew product

Indexed keywords

EID: 18144381949     PISSN: 00162663     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10688-005-0014-8     Document Type: Article

References (19)

1. R. Abraham and S. Smale, "Nongenericity of Ω-stability," In: Global Analysis (Proc. Sympos. Pure Math., Vol. XIV, Berkeley, Calif., 1968), Amer. Math. Soc., Providence, R.I., 1970, pp. 5-8.
2. Ya. Pesin, "Characteristic Lyapunov exponents and smooth ergodic theory," Usp. Mat. Nauk, 32, No. 4 (196), 55-112 (1977).
3. J. Bochi, "Genericity of zero Lyapunov exponents," Ergodic Theory Dynam. Systems, 22, No. 6, 1667-1696 (2002).
4. J. Bochi and M. Viana, "Uniform (projective) hyperbolicity or no hyperbolicity: a dichotomy for generic conservative maps," Ann. Inst. H. Poincare Anal. Non Liniaire, 19, No. 1, 113-123 (2002).
5. A. Baraviera and C. Bonatti, "Removing zero Lyapunov exponents," Ergodic Theory Dynam. Systems, 23, 1655-1670 (2003).
6. M. Shub and A. Wilkinson, "Pathological foliations and removable zero exponents," Invent. Math., 139, 495-508 (2000).
7. D. Dolgopyat and Y. Pesin, "Every compact manifold carries a completely hyperbolic diffeomorphism," Ergodic Theory Dynam. Systems, 22, No. 2, 409-435 (2002).
8. M. W. Hirsch, C. C. Pugh, and M. Shub, Invariant Manifolds, Lect. Notes in Math., Vol. 583, Springer-Verlag, Berlin-New York, 1977.
9. A. Gorodetski and Yu. Ilyashenko, "Some new robust properties of invariant sets and attractors of dynamical systems," Funkts. Anal. Prilozhen., 33, No. 2, 16-30 (1999).
10. A. Gorodetski and Yu. Ilyashenko, "Some properties of skew products over the horseshoe and solenoid," Trudy MIRAN, 231, 6-118 (2000);
11. English transl. Proc. Steklov Inst. Math., 231, 96-118 (2000).
12. A. Gorodetski, Minimal Attractors and Partially Hyperbolic Invariant Sets of Dynamical Systems, PhD thesis, Moscow State University, 2001.
13. V. Kleptsyn and M. Nalsky, "Contraction of Orbits in Random Dynamical Systems on the Circle," Funkts. Anal. Prilozhen., 38, No. 4, 36-54 (2004).
14. A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis. Vol. 2: Measure. The Lebesgue integral. Hilbert space, Graylock Press, Albany, N.Y., 1961.
15. Yu. Ilyashenko and W. Li, Nonlocal Bifurcations, Amer. Math. Soc., Providence, R.I., 1999.
16. A. Katok and B. Hasselblat, Introduction to the Modern Theory of Dynamical System, Cambridge Univ. Press, 1995.
17. A. Katok and A. Stepin, "Approximation of ergodic dynamical systems by periodic transformations," Dokl. Akad. Nauk SSSR, 171, 1268-1271 (1966);
18. English transl. Soviet Math. Dokl, 7, 1638-1641 (1966).
19. A. Katok and A. Stepin, "Approximations in ergodic theory," Usp. Mat. Nauk., 22, No. 5 (137), 81-106 (1967).