Mathematical Sciences: Theory and Application of Linear     Ordinary Differential Equations
{'Code': '03040103', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
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This project is mathematical research on linear differential               operators.  Such operators transform spaces of functions by                     taking derivatives and multiplying by coefficients.  They are                   often used to represent physical systems.  In this situation,                   their spectrum, a set of numbers determined by how the operator                 acts on the space, corresponds to possible energy levels of the                 system.                                                                              More specifically, Professor Johnson will study linear                     ordinary differential operators with bounded but non-decaying                   coefficients (which might be almost periodic, or might be typical               paths of a stationary ergodic process).  Using techniques from                  dynamical systems theory, he will study spectral properties and                 generalized Floquet exponents for such operators.  He will apply                his results to the following areas among others:  bifurcation                   from invariant tori in nonlinear dynamical systems;  the Korteweg               -deVries equation with bounded initial data;  relations of this                 to string theory via the Virasoro algebra;  the topological index               theory of periodic and non-periodic differential equations, and                 its relation with the homology theory of certain operator                       algebras.
{'FirstName': 'Russell', 'LastName': 'Johnson', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Russell Johnson', 'EmailAddress': None, 'NSF_ID': '000383790', 'StartDate': '06/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Southern California', 'CityName': 'LOS ANGELES', 'ZipCode': '90033', 'PhoneNumber': '2137407762', 'StreetAddress': '3720 S FLOWER ST FL 3', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'California', 'StateCode': 'CA', 'CONGRESSDISTRICT': '34', 'CONGRESS_DISTRICT_ORG': 'CA34', 'ORG_UEI_NUM': 'G88KLJR3KYT5', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF SOUTHERN CALIFORNIA', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '126200', 'Text': 'MODERN ANALYSIS'}
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