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  • Birkhoff's problem  (1)
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    Electronic Resource
    Electronic Resource
    Cross Sections in the Three-Body Problem (2000)
    Springer
    Journal of dynamics and differential equations 12 (2000), S. 247-271 
    Details
    ISSN: 1572-9222
    Keywords: Birkhoff's problem ; cross section ; three-body problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In Dynamical Systems, Birkhoff gave a clear formulation of a cross section, suggested a possible generalization to cross sections with boundary, and raised the question of whether or not such cross sections exist in the three-body problem. In this work, we explicitly develop Birkhoff's notion of a generalized cross section, formulate homological necessary conditions for the existence of a cross section or generalized cross section, and show that these conditions are not satisfied in the three-body problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1009007007669
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