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  • Differential delay equations  (1)
  • numerically computed orbits  (1)
  • 1
    Electronic Resource
    Electronic Resource
    On the numerical computation of orbits of dynamical systems: The one-dimensional case (1991)
    Springer
    Journal of dynamics and differential equations 3 (1991), S. 361-379 
    Details
    ISSN: 1572-9222
    Keywords: Dynamical systems ; numerically computed orbits ; shadowing ; pseudo-orbits ; round-off ; expansiveness
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A finite time version of the shadowing theorem is used to develop a procedure to determine the accuracy of numerically computed orbits of one-dimensional maps. The procedure works forward. After any given number of iterates, we can decide whether our theorem applies and, if it does, we can estimate how far the computed orbit is from a true orbit.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01049737
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Transition layers for singularly perturbed delay differential equations with monotone nonlinearities (1989)
    Springer
    Journal of dynamics and differential equations 1 (1989), S. 3-43 
    Details
    ISSN: 1572-9222
    Keywords: Differential delay equations ; singular perturbations ; transition layers
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Transition layers arising from square-wave-like periodic solutions of a singularly perturbed delay differential equation are studied. Such transition layers correspond to heteroclinic orbits connecting a pair of equilibria of an associated system of transition layer equations. Assuming a monotonicity condition in the nonlinearity, we prove these transition layer equations possess a unique heteroclinic orbit, and that this orbit is monotone. The proof involves a global continuation for heteroclinic orbits.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01048789
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    Paper (German National Licenses)
    Fulltext
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