Mathematical Sciences: Aspects of Anosov Systems
{'Code': '03040108', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'James Glazebrook', 'PO_EMAI': None, 'PO_PHON': None}
This research will focus on the study of the dynamics of                   manifolds. Interest in this topic stems principally from                        Thurston's work on the classification of diffeomorphisms of                     surfaces. The questions to be addressed concern invariant sets of               automorphisms of torii, flows on surfaces of negative curvature                 and diffeomorphisms of Lorenz manifolds.                                             Albert Fathi will use his knowledge of pseudo-Anosov flows                 to construct and investigate compact invariant subsets of                       hyperbolic toral maps. In particular he will investigate                        estimates for the Hausdorff dimension of these sets. Fathi will                 also continue his investigations of the connections between the                 intersection of geodesic currents and metric entropy. The final                 part of the project involves the study of Anosov diffeomorphisms                of Lorenz manifolds. The objective here is to try to extend                     established results about flows on Riemannian manifolds of                      negative curvature to time-like geodesic flow on certain Lorenz                 manifolds. Special attention will be devoted to those manifolds                 of importance in general relativity.
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{'Name': 'University of Florida', 'CityName': 'GAINESVILLE', 'ZipCode': '326111941', 'PhoneNumber': '3523923516', 'StreetAddress': '1523 UNION RD RM 207', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Florida', 'StateCode': 'FL', 'CONGRESSDISTRICT': '03', 'CONGRESS_DISTRICT_ORG': 'FL03', 'ORG_UEI_NUM': 'NNFQH1JAPEP3', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF FLORIDA', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '126500', 'Text': 'GEOMETRIC ANALYSIS'}
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