Life expectancy of transient microchaotic behaviour

Journal of Nonlinear Science

Volumn 15, Issue 2, 2005, Pages 63-91

  Csernak G ^a   Stepan G ^a  

^a BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS   (Hungary)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84867978564     PISSN: 09388974     EISSN: 14321467     Source Type: Journal    
DOI: 10.1007/s00332-004-0620-2     Document Type: Article

References (16)

1. J. A. Yorke, E. D. Yorke, Metastable Chaos: The Transition to Sustained Chaotic Behavior in the Lorenz Model, J. Stat. Phys., 21 (3), 1979.
2. T. T'el, Transient Chaos, published in Directions in Chaos, vol. 3, edited by Hao Bai-lin, World Scientific Publishing Company, Singapore, pp. 149-211, 1990.
3. G. Pianigiani, J. A. Yorke, Expanding Maps on Sets which Are Almost Invariant: Decay and Chaos, Trans. Am. Math. Soc., 252, pp. 351-366, 1979.
4. A. Lasota, J. A. Yorke, The Law of Exponential Decay for Expanding Mappings, Rend. Sem. Math. Univ. Padova, 64, pp. 141-157, 1981.
5. H. van den Bedem, N. Chernov, Expanding Maps of an Interval with Holes, Ergodic Theory Dynam. Syst., 22 (3), pp. 637-654, 2002.
6. G. Cserńak, G. Stepan, Fractal Dimension as Measure of Control Time, Periodica Polytechnica Ser. Mech. Eng., 48 (1), pp. 17-25, 2004.
7. G. Haller, G. Stepan, Micro-Chaos in Digital Control, J. Nonlinear Sci., 6, pp. 415-448, 1996. (Pubitemid 126429514)
8. E. Enikov, G. Stepan, Micro-Chaotic Motion of Digitally Controlled Machines, J. Vibration and Control, 4, pp. 427-443, 1998. (Pubitemid 128579117)
9. R. Klages, J. R. Dorfman, Simple Maps with Fractal Diffusion Coefficients, Phys. Rev. Lett. 74, pp. 387-390, 1995.
10. P. Cvitanovíc et al. Classical and Quantum Chaos, www.nbi.dk/ChaosBook, Niels Bohr Institute, Copenhagen, 2001.
11. V. Lakshmikantham, D. Trigiante, Theory of Difference Equations-Numerical Methods and Applications, Academic Press, San Diego, 1988.
12. P. Collet, J.-P. Eckmann, Iterated Maps on the Interval as Dynamical Systems, Birkḧauser, Boston, 1980.
13. G. Cserńak, G. Stepan, Life Expectancy Calculations of Transient Chaotic Behaviour Using Approximate 1D Maps, Meccanica 35 (6), pp. 547-562, 2000. (Pubitemid 32827312)
14. G. Cserńak, G. Stepan, Escape Rate of Transient Chaotic Phenomena in Digitally Controlled Systems, Proceedings of the Fifth World Congress on Computational Mechanics, online publication, Vienna University of Technology, Austria, ISBN 3-9501554-0-6, http://wccm.tuwien.ac.at, Vienna, 2002.
15. E. Ott, Chaos in Dynamical Systems, Cambridge University Press, Cambridge, 1993.
16. B. Mandelbrot, Fractals: Form, Chance, and Dimension, Freeman, San Francisco, 1977.