A Computer-Assisted Approach to Small-Divisors Problems Arising in Hamiltonian Mechanics

  • Alessandra Celletti
  • Luigi Chierchia
Part of the The IMA Volumes in Mathematics and Its Applications book series (IMA, volume 28)


One of the most powerful and versatile tools in the study of invariant surfaces for conservative dynamical systems relies upon KAM theory ([14], [1], [16], [17], [7], [19], [12], [20]). However, because of the apparently stringent quantitative requirements, such theory has been (and often still is) considered not too well suited for concrete applications. Nevertheless, in [3], [5], [6], [21] and especially in [4], [18], [9], [2], it has been shown how refinements and implementations of KAM theory may yield quantitative rigorous results that are in good agreement with the numerical expectations.


Interval Arithmetic Elementary Operation Invariant Curf Invariant Surface Initial Approximant 
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Copyright information

© Springer-Verlag New York Inc. 1991

Authors and Affiliations

  • Alessandra Celletti
    • 1
  • Luigi Chierchia
    • 2
  1. 1.Forschungsinstitut für MathematikETH-ZentrumZürichSwitzerland
  2. 2.Dipartimento di MatematicaII Universita’ di RomaRomaItalia

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