An ultimate bound on the trajectories of the lorenz system and its applications

Nonlinearity

Volumn 16, Issue 5, 2003, Pages 1597-1605

  Pogromsky, A Yu ^a   Santoboni, G ^b   Nijmeijer, H ^a  

^a EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b UNIVERSITY OF CAGLIARI   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0142168383     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/16/5/303     Document Type: Article

References (9)

1. Ashwin P, Buescu J and Stewart I 1996 From attractor to chaotic saddle: a tale of transverse instability Nonlinearity 9 703-37
2. Eden A 1989 Local Lyapunov exponents and a local estimate of Hausdorff dimension Math. Model. Numer. Anal. 23 405-13
3. Hunt B R and Ott E 1996 Optimal periodic orbits of chaotic systems occur at low period Phys. Rev. E 54 328-37
4. Leonov G A, Ponomarenko D V and Smirnova V B 1996 Frequency-Domain Methods for Nonlinear Analysis (Singapore: World Scientific)
5. Ljashko A S 1994 Estimates for fractal and Hausdorff dimensions of invariant sets of dynamical systems PhD Thesis Department of Mathematics and Mechanics, St Petersburg State University, Russia
6. Leonov G A 2001 Lyapunov dimension formulas for Henon and Lorenz attractors St Petersburg Math. J. 13 1-12
7. Pogromsky A Yu and Nijmeijer H 2000 On estimates of the Hausdorff dimension of invariant compact sets Nonlinearity 13 927-45
8. Swinnerton-Dyer P 2001 Bounds for trajectories of the Lorenz equations: an illustration of how to choose Liapunov functions Phys. Lett. A 281 161-7
9. Tucker W 2002 A Rigorous ODE solver and Smale's 14th problem Foundations Comput. Math. 2 53-117