Monotonic dynamical systems under spatial discretization
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- by P. Diamond, P. Kloeden, V. Kozyakin and A. Pokrovskii PDF
- Proc. Amer. Math. Soc. 126 (1998), 2169-2174 Request permission
Abstract:
We estimate the probability of replicating the asymptotic behaviour of a dynamical system generated by a monotonic mapping for randomly centered roundoff lattices.References
- C. Beck and G. Roepstorff, Effects of phase space discretization on the long-time behavior of dynamical systems, Phys. D 25 (1987), no. 1-3, 173–180. MR 887462, DOI 10.1016/0167-2789(87)90100-X
- Abraham Berman and Robert J. Plemmons, Nonnegative matrices in the mathematical sciences, Classics in Applied Mathematics, vol. 9, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1994. Revised reprint of the 1979 original. MR 1298430, DOI 10.1137/1.9781611971262
- P. M. Binder, Machine iteration of a linear function: local behaviour, Comput. Math. Appl. 21 (1991), no. 2-3, 133–140. MR 1088787, DOI 10.1016/0898-1221(91)90091-H
- Garrett Birkhoff, Lattice theory, 3rd ed., American Mathematical Society Colloquium Publications, Vol. XXV, American Mathematical Society, Providence, R.I., 1967. MR 0227053
- Michael Blank, Pathologies generated by round-off in dynamical systems, Phys. D 78 (1994), no. 1-2, 93–114. MR 1299502, DOI 10.1016/0167-2789(94)00103-0
- J.J.F. Cavanagh, Digital Computer Arithmetic. Design and Implementation, McGraw–Hill Book Company, 1984.
- Morris W. Hirsch, The dynamical systems approach to differential equations, Bull. Amer. Math. Soc. (N.S.) 11 (1984), no. 1, 1–64. MR 741723, DOI 10.1090/S0273-0979-1984-15236-4
- M. G. Kendall and P. A. P. Moran, Geometrical probability, Griffin’s Statistical Monographs & Courses, No. 10, Hafner Publishing Co., New York, 1963. MR 0174068
- M. A. Krasnosel′skiĭ, Positive solutions of operator equations, P. Noordhoff Ltd., Groningen, 1964. Translated from the Russian by Richard E. Flaherty; edited by Leo F. Boron. MR 0181881
- M. A. Krasnosel′skiĭ and A. V. Pokrovskiĭ, Regular solutions of equations with discontinuous nonlinearities, Dokl. Akad. Nauk SSSR 226 (1976), no. 3, 506–509 (Russian). MR 0637075
- M. A. Krasnosel′skiĭ and P. P. Zabreĭko, Geometrical methods of nonlinear analysis, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 263, Springer-Verlag, Berlin, 1984. Translated from the Russian by Christian C. Fenske. MR 736839, DOI 10.1007/978-3-642-69409-7
- A. V. Pokrovskiĭ, Correct solutions of equations with strong nonlinearities, Dokl. Akad. Nauk SSSR 274 (1984), no. 5, 1037–1040 (Russian). MR 734938
- Hal L. Smith, Monotone dynamical systems, Mathematical Surveys and Monographs, vol. 41, American Mathematical Society, Providence, RI, 1995. An introduction to the theory of competitive and cooperative systems. MR 1319817
- Hans J. Stetter, Analysis of discretization methods for ordinary differential equations, Springer Tracts in Natural Philosophy, Vol. 23, Springer-Verlag, New York-Heidelberg, 1973. MR 0426438, DOI 10.1007/978-3-642-65471-8
Additional Information
- P. Diamond
- Affiliation: Department of Mathematics, University of Queensland, Brisbane 4072, Australia
- Email: pmd@maths.uq.edu.au
- P. Kloeden
- Affiliation: Fachbereich Mathematik, Johann Wolfgang Goethe Universitat, D-60054 Frankfurt am Main, Germany
- MR Author ID: 102990
- Email: kloeden@math.uni-frankfurt.de
- V. Kozyakin
- Affiliation: Institute of Information Transmission Problems, Russian Academy of Science, 19 Ermolovoy St., Moscow 101447, Russia
- Email: kozyakin@nov.ippi.ras.ru
- A. Pokrovskii
- Affiliation: Physics Department, University College, Cork, Ireland
- Received by editor(s): September 23, 1996
- Received by editor(s) in revised form: December 24, 1996
- Additional Notes: This research was supported by the Australian Research Council Grant A 8913 2609.
- Communicated by: Hal L. Smith
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 2169-2174
- MSC (1991): Primary 58F10, 58F12
- DOI: https://doi.org/10.1090/S0002-9939-98-04277-4
- MathSciNet review: 1443379