Monotonic dynamical systems under spatial discretization

Proceedings of the American Mathematical Society

Volumn 126, Issue 7, 1998, Pages 2169-2174

  Diamond, P ^a   Kloeden, P ^b   Kozyakin, V ^c   Pokrovskii, A ^d  

^a UNIVERSITY OF QUEENSLAND   (Australia)

^b GOETHE UNIVERSITY   (Germany)

^c INSTITUTE FOR INFORMATION TRANSMISSION PROBLEMS   (Russian Federation)

^d UNIVERSITY COLLEGE CORK   (Ireland)

Author keywords

Asymptotic stability; Dynamical system; Roundoff lattice

Indexed keywords

EID: 22044458691     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9939-98-04277-4     Document Type: Article

References (14)

1. C. Beck and G. Roepstorff, Effects of Phase Space Discretization on the Long-time Behaviour of Dynamical Systems. Physica , D25 (1987), 173-180. MR 881:58152
2. A. Berman and R.J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, SIAM Classics in Applied Math. vol. 9, SIAM, Philadelphia, 1994. MR 95e:15013
3. P.M. Binder, Machine iteration of a linear mapping: Local behaviour, Computers Math. Applic., 21 (1991), 133-140. MR 91m:58084
4. G. Birkhoff, Lattice Theory, AMS. Colloq. Publ. vol 25., Amer. Math. Soc., Providence (1967). MR 37:2638
5. M. Blank, Pathologies generated by round-off in dynamical systems, Physica D 78, 93-114 (1994). MR 95g:58115
6. J.J.F. Cavanagh, Digital Computer Arithmetic. Design and Implementation, McGraw-Hill Book Company, 1984.
7. M.W. Hirsch, The dynamical systems approach to differential equations, Bulletin of AMS, 11 (1984), 1-64. MR 85m:58060
8. M.G. Kendall and P.A.P. Moran, Geometrical Probability, C. Griffin, London (1963). MR 30:4275
9. M.A. Krasnosel'skii, Positive Solutions of Operator Equations, Noordhoff, Groningen, 1964. MR 31:6107
10. M.A. Krasnosel'skii and A.V. Pokrovskii, Regular solutions of equations with discontinuous nonlinearities. Soviet Mathematics, 17 (1976), 128 - 132. MR 58:30559
11. M.A. Krasnosel'skii and P.P. Zabreiko, Geometrical Methods of Nonlinear Analysis, Springer-Verlag, Berlin, 1984. MR 85b:47057
12. A.V. Pokrovskii:'Correct solutions of equations with strong nonlinearities. Soviet Mathematics Doklady, 29 (1984), 107 - 110. MR 8Gc:35056
13. H.L. Smith, Monotone Dynamical Systems, Amer. Math. Soc., Providence, RI, 1995. MR 96c:34002
14. H.J. Stetter, Analysis of Discretization Methods for Ordinary Differential Equations, Springer-Verlag, Berlin (1973). MR 54:14381