An adaptive method for the approximation of the generalized cell mapping

Chaos, Solitons and Fractals

Volumn 8, Issue 4 SPEC. ISS., 1997, Pages 525-534

  Guder, Rabbijah ^a   Dellnitz, Michael ^b   Kreuzer, Edwin ^b  

^a HAMBURG UNIVERSITY OF TECHNOLOGY   (Germany)

^b UNIVERSITY OF BAYREUTH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000557301     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0960-0779(96)00118-x     Document Type: Article

References (12)

1. Hsu, H. S., Global analysis by cell mapping. Internat. J. Bifur. Chaos, 1992, 2, 727-771.
2. Kreuzer, E., Numerische Untersuchung nichtlinearer dynamischer Systeme. Springer, Berlin, 1987.
3. Tongue, B. H., On obtaining global nonlinear system characteristics through interpolated cell mapping. Phys. D, 1987, 28, 401-408.
4. van der Speck, J., Cell mapping methods: modifications and extensions. Ph.D. thesis, Technical University of Eindhoven, 1994.
5. Guder, R. and Kreuzer, E., Using the generalized cell mapping to approximate invariant measures on compact manifolds, 1997, to appear.
6. Hunt, F. Y., A Monte-Carlo approach to the approximation of invariant measures. National Institute of Standards and Technology, NISTIR, 1993, 4980.
7. Bestie, D. & Kreuzer, E., A modification and extension of an algorithm for generalized cell mapping. Comput. Methods Appl. Mech. Engrg, 1986, 59, 1-9.
8. Hsu, H. S., A theory of cell-to-cell mapping dynamical systems. J. Appl. Mech., 1980, 47, 931-939.
9. Mane, R., Ergodic Theory and Differentiable Dynamics. Springer, Berlin, 1987.
10. Lasota, A. and Mackey, C., Chaos, Fractals and Noise. Springer, Berlin, 1994.
11. Li, T. Y., Finite approximation of the Frobenius-Perron operator, a solution to Ulam's conjecture. J. Approx. Theory, 1976, 17, 177-186.
12. Dellnitz, M., Hohmann, A., Junge, O. and Rumpf, M., Exploring invariant sets and invariant measures, 1997, submitted.