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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