Paper

Forward boundedness of the trace map for the period doubling substitution

Published 21 July 2020 • © 2020 IOP Publishing Ltd & London Mathematical Society
, , Citation T O Carvalho 2020 Nonlinearity 33 4390 DOI 10.1088/1361-6544/ab8d17

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tuliocarvalho@uel.br

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1 Departamento de Matemática, UEL, CP 10011, Londrina, PR, 86057-970, Brazil

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Dates

  1. Received 4 June 2019
  2. Revised 17 April 2020
  3. Accepted 24 April 2020
  4. Published

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0951-7715/33/9/4390

Abstract

We study the trace map for the period doubling substitution, proving its orbits are forward bounded, a sufficient condition for application in the study of spectral measures. This result is in contrast with some recent findings of unbounded orbits on the trace map for the Thue–Morse substitution.

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10.1088/1361-6544/ab8d17