Mathematical Sciences: Fractal Geometry and the Dynamics of Finitely Differentiable Maps
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Alec Norton will work on problems related to the dynamical                 behaviour of differentiable mappings in two dimensions. These in                turn are closely related to questions about the nature of the                   critical sets of differentiable functions. For example,                         information about the size of the image of a critical set can be                obtained from the degree of differentiability of the function                   concerned. Results such as these are closely related to the                     Morse-Sard theorem. These investigations are in many ways                       complementary to the more established works on conformal                        dynamics.                                                                            Although the Morse-Sard has been used extensively as an                    analytic tool, Norton will be investigating its geometric                       ramifications. In particular he will use it to study the                        loxodromic mapping problem. This asks for diffeomorphisms of the                two dimensional sphere for which the poles satisfy certain                      properties. Previous work has shown that the degree of                          differentiability of the function plays an important role in                    these questions. In a slightly different direction he will try to               extend known results about Denjoy dynamics on the circle to the                 torus.
{'FirstName': 'Alec', 'LastName': 'Kercheval', 'PI_MID_INIT': 'N', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Alec N Kercheval', 'EmailAddress': 'kercheva@math.fsu.edu', 'NSF_ID': '000460496', 'StartDate': '07/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
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{'Code': '1265', 'Text': 'GEOMETRIC ANALYSIS'}
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