In this paper we consider the sequence of Kakutani’s -refinements corresponding to the inverse of the golden ratio (which we call the Kakutani–Fibonacci sequence of partitions) and associate to it an ergodic interval exchange (which we call the Kakutani–Fibonacci transformation) using the ‘cutting–stacking’ technique. We prove that the orbit of the origin under this map coincides with a low discrepancy sequence (which we call the Kakutani–Fibonacci sequence of points), which has also been considered by other authors.

A dynamical system approach to the Kakutani-Fibonacci sequence

CARBONE, Ingrid;
2014

Abstract

In this paper we consider the sequence of Kakutani’s -refinements corresponding to the inverse of the golden ratio (which we call the Kakutani–Fibonacci sequence of partitions) and associate to it an ergodic interval exchange (which we call the Kakutani–Fibonacci transformation) using the ‘cutting–stacking’ technique. We prove that the orbit of the origin under this map coincides with a low discrepancy sequence (which we call the Kakutani–Fibonacci sequence of points), which has also been considered by other authors.
Kakutani-Fibonacci sequence; Ergodic theory and uniform distribution; von Neumann-Kakutani transformation
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11770/138555
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