This article is available for purchase or by subscription. See below.
Abstract
|
The Lévy constant of an irrational real number is defined by the exponential growth rate
of the sequence of denominators of the principal convergents in its continued fraction
expansion. Any quadratic irrational has an ultimately periodic continued fraction
expansion and it is well-known that this implies the existence of a Lévy constant. Let
be distinct
positive integers. If the sequence of partial quotients of an irrational real number is a Sturmian
sequence over
,
then it has a Lévy constant, which depends only on
,
,
and the slope of the Sturmian sequence, but not on its intercept. We show
that the set of Lévy constants of irrational real numbers whose sequence
of partial quotients is periodic or Sturmian is equal to the whole interval
.
|
PDF Access Denied
We have not been able to recognize your IP address
44.200.23.133
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our
journal-recommendation form.
Or, visit our
subscription page
for instructions on purchasing a subscription.
You may also contact us at
contact@msp.org
or by using our
contact form.
Or, you may purchase this single article for
USD 40.00:
Keywords
continued fraction, Lévy constant, Sturmian word,
mechanical word, quasi-Sturmian word
|
Mathematical Subject Classification
Primary: 11A55
Secondary: 68R15
|
Milestones
Received: 20 April 2020
Revised: 23 July 2021
Accepted: 17 September 2021
Published: 13 December 2021
|
|