Control of an adaptive refinement technique of generalized cell mapping by system dynamics

Nonlinear Dynamics

Volumn 20, Issue 1, 1999, Pages 21-32

  Guder, Rabbijah ^a   Kreuzer, Edwin ^a  

^a HAMBURG UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

DYNAMICS; MATHEMATICAL MODELS; NUMERICAL ANALYSIS;

ADAPTIVE REFINEMENT; GENERALIZED CELL MAPPING; NONLINEAR DYNAMIC SYSTEMS;

NONLINEAR SYSTEMS;

EID: 0032595367     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008352418599     Document Type: Article

References (12)

1. Dellnitz, M. and Junge, O., 'An adaptive subdivision technique for the approximation of attractors and invariant measures', Computing and Visualization in Science 1, 1998, 63-68.
2. Dellnitz, M. and Junge, O., 'On the approximation of complicated dynamical behavior', SIAM Journal on Numerical Analysis, 1998, to appear.
3. Guder, R. and Kreuzer, E., 'Using the generalized cell mapping to approximate invariant measures on compact manifolds', International Journal of Bifurcation and Chaos 7(11), 1997, 2487-2499.
4. Guder, R., Dellnitz, M., and Kreuzer, E., 'An adaptive method for the approximation of the generalized cell mapping', Chaos, Solitons and Fractals 8(4), 1997, 525-534.
5. Hsu, C. S., 'A theory of cell-to-cell mapping dynamical systems', Journal of Applied Mechanics 47, 1980, 931-939.
6. Hsu, C. S., Cell-to-Cell Mapping - A Method of Global Analysis for Nonlinear Systems, Springer-Verlag, New York, 1987.
7. Hsu, C. S., 'Global analysis by cell mapping', International Journal of Bifurcation and Chaos 2, 1992, 727-771.
8. Hunt, F. Y., 'A Monte-Carlo approach to the approximation of invariant measures', National Institute of Standards and Technology Report, No. 4980, 1993.
9. Kreuzer, E., Numerische Untersuchung nichtlinearer dynamischer Systeme, Springer-Verlag, Berlin, 1987.
10. Lasota, A. and Mackey C., Chaos, Fractals and Noise, Springer-Verlag, New York, 1994.
11. Li, T. Y., 'Finite approximation of the Frobenius-Perron operator, a solution to Ulam's conjecture', Journal of Approximation Theory 17, 1976, 177-186.
12. Tongue, B. H. and Gu, K., 'Adaptive mesh strategies for interpolated mapping procedure', International Journal of Engineering Science 21(10), 1989, 1143-1154.