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Backward Continued Fractions and their Invariant Measures

Published online by Cambridge University Press:  20 November 2018

Karlheinz Gröchenig  and
Andrew Haas
Karlheinz Gröchenig
Affiliation:
Department of Mathematics, The University of Connecticut, Storrs, Connecticut 06269-3009, U.S.A. e-mail:GROCH@MATH.UCONN.EDUe-mail:HAAS@MATH.UCONN.EDU
Andrew Haas
Affiliation:
Department of Mathematics, The University of Connecticut, Storrs, Connecticut 06269-3009, U.S.A. e-mail:GROCH@MATH.UCONN.EDUe-mail:HAAS@MATH.UCONN.EDU
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Abstract

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This paper continues our investigation of backward continued fractions, associated with the generalized Renyi maps on [0,1). We first show that the dynamics of the shift map on a specific class of shift invariant spaces of nonnegative integer sequences exactly models the maps Tu for u € (0,4). In the second part we construct a new family of explicit invariant measures for certain values of the parameter u.

Keywords

11J7058F1158F03Continued fractionsinterval mapsinvariant measuressymbolic dynamics
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 39 , Issue 2 , 01 June 1996 , pp. 186 - 198
Copyright
Copyright © Canadian Mathematical Society 1996

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