Mathematical Sciences: Accurate Perturbative Bounds in      K.A.M.
{'Code': '03040103', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'William Y. Velez', 'PO_EMAI': None, 'PO_PHON': None}
This project is mathematical research in perturbation theory                for problems in classical mechanics and related areas.  The                     essential difficulty to be overcome is that one is working near                 resonances that lead to very large terms in the perturbation                    expansion.  These are overcome by the techniques of the so-called               K.A.M. theory, which gives a more sophisticated way of handling                 such perturbations.  The numerical bounds given by a                            straightforward application of K.A.M. are not sharp.  The main                  objective of the present project is to sharpen the bounds to                    values that are close to best possible.  The method is to explore               various strategies for obtaining the bounds by use of a computer                program that automates the process of finding rigorous bounds                   through the use of a sort of interval arithmetic in Banach spaces               of functions.
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[{'Code': '1262', 'Text': 'MODERN ANALYSIS'}, {'Code': '1271', 'Text': 'COMPUTATIONAL MATHEMATICS'}, {'Code': '2865', 'Text': 'NUMERIC, SYMBOLIC & GEO COMPUT'}]
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