60 years of dynamics and number expansions

A curious property of the Pell sequence

speaker: Mike Keane (Delft University of Technology)

abstract: In joint yet unpublished work with Michel Dekking, we show that the 0-1 infinite sequence produced by the Pell substitution

0->001 1->0

starting with 0 is equal to the 0-1 infinite sequence produced by the yet unknown infinite sequence produced by the iteration of the block replacement

00-> 0010 01-> 001 10-> 010

starting with either 00 or with 01, which we call kappa. Note that kappa cannot be iterated, yet still obviously produces a unique infinite sequence. This describes a recent attempt to understand the sequence produced by the block replacement

00-> 0011 01-> 001 10-> 011 11 ->01,

whose behaviour is yet beyond our comprehension, unlike Pell.

timetable:
Mon 10 Dec, 17:15 - 18:00, Aula Dini
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