Mathematical Sciences: Stable Classification and            Automorphisms of Shift Dynamical Systems
{'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 award will support the mathematical research of                        Professors Kim and Roush in a branch of ergodic theory called                   symbolic dynamics.  A symbolic dynamical system is a collection                 of two-way infinite strings of symbols from a finite alphabet                   satisfying a formation rule that specifies which symbols are                    allowed to follow which as one moves along the string.  Two such                systems are equivalent if there is a well-behaved bijection                     between them that respects the operation of shifting.  A central                theme in this area is the classification of symbolic dynamical                  systems with respect to various forms of equivalence. Symbolic                  dynamical systems have recently found widespread application in                 the modeling of data transmission.                                                   The principal investigators will study strong shift                        equivalence over the positive integers, over the rationals, and                 over general rings, and strong sofic shift equivalence over the                 rationals. They will also consider automorphisms of shift                       dynamical systems, in particular periodic points, enumeration of                automorphisms, and subgroups of the automorphism group.
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{'Code': '126200', 'Text': 'MODERN ANALYSIS'}
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