Normal Lyapunov exponents and asymptotically stable attractors

Dynamical Systems

Volumn 23, Issue 2, 2008, Pages 207-218

  Xu, Lan ^a   Chen, Beimei ^a   Zhao, Yun ^b   Cao, Yongluo ^b  

^a SUZHOU VOCATIONAL UNIVERSITY   (China)

^b SOOCHOW UNIVERSITY   (China)

Author keywords

Asymptotically stable attractors; Ergodic measure; Normal Lyapunov exponents

Indexed keywords

ASYMPTOTICALLY STABLE; LYAPUNOV EXPONENT (LE);

DIFFERENTIAL EQUATIONS;

EID: 46249089477     PISSN: 14689367     EISSN: 14689375     Source Type: Journal    
DOI: 10.1080/14689360802058765     Document Type: Article

References (12)

1. V.I. Oseledec, A multiplicative ergodic theorem, Characteristic Ljapunov, exponents of dynamical systems, Transactions of the Moscow Mathematical Society, Vol. 19, American Mathematical Society, Providence, R.I., 1968.
2. P. Ashwin, J. Buescu, and I. Stewart, Bubbling of attractors and synchronization of oscillators, Phys. Lett. A 193 (1994), pp. 126-139.
3. _, From attractor to chaotic saddle: a tale of transverse instability, Nonlinearity 9 (1996), pp. 703-737.
4. K. Josic, Synchronization of chaotic systems and invariant manifold, Nonlinearity 13 (2000), pp. 1321-1336.
5. N. Fenichel, Persistence and smoothness of invariant manifolds for flows, Indiana Univ. Math. J. 2 (1971), pp. 193-226.
6. L.B. Ryashko and E.E. Shnol, On exponentially attracting invariant manifold of ODEs, Nonlinearity 16 (2003), pp. 147-160.
7. Cao Yongluo and Xu Lan, A note about exponentially attracting invariant manifold of ODEs, Nonlinearity 18 (2005), pp. 2727-2736.
8. O. Jenkinson, Ergodic optimization, Discrete Contin. Dynam. Systems 15 (2006), pp. 197-224.
9. O. Jenkinson, R. Mauldin, and M. Urbanski, Ergodic optimization for noncompact dynamical systems, Dynam. Systems 22 (2007), pp. 379-388.
10. 1 expanding maps of the circle, preprint (2007).
11. P. Walters, An Introduction to Ergodic Theory, Springer-Verlag Press, New York, 1981.
12. G. Yuan and B.R. Hunt, Optimal orbits of hyperbolic systems, Nonlinearity 12 (1999), pp. 1207-1224.