An approach to renormalization on the n-torus |
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| Authors: | Rockmore Daniel Siegel Ralph Tongring Nils Tresser Charles |
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| Institution: | Department of Mathematics, Columbia University, New York, New York 10027IBM, Thomas J. Watson Research Center, Yorktown Heights, New York 10598Center for Molecular and Behavioral Neuroscience, Rutgers University, Newark, New Jersey 01579The Graduate School and University Center, City University of New York, New York, New York 10036-8099IBM, Thomas J. Watson Research Center, Yorktown Heights, New York 10598. |
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| Abstract: | The coding theory of rotations (by inspecting closely their relation to flows) and the continued fractions algorithm (by considering even two-coloring of the integers with a given proportion of, say, blue and red) are revisited. Then, even n-coloring of the integers is defined. This allows one to code rotations on the (n-1)-torus by considering linear flows on the n-torus and yields a simple geometric approach to renormalization on tori by first return maps on the coding regions. |
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