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Conformal Geometry and Dynamics

Published by the American Mathematical Society, the Conformal Geometry and Dynamics (ECGD) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.5.

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Hilbert spaces of martingales supporting certain substitution-dynamical systems
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by Dorin Ervin Dutkay and Palle E. T. Jorgensen PDF
Conform. Geom. Dyn. 9 (2005), 24-45 Request permission

Abstract:

Let $X$ be a compact Hausdorff space. We study finite-to-one mappings $r\colon X\rightarrow X$, onto $X$, and measures on the corresponding projective limit space $X_\infty (r)$. We show that certain quasi-invariant measures on $X_\infty (r)$ correspond in a one-to-one fashion to measures on $X$ which satisfy two identities. Moreover, we identify those special measures on $X_\infty (r)$ which are associated via our correspondence with a function $V$ on $X$, a Ruelle transfer operator $R_V$, and an equilibrium measure $\mu _V$ on $X$.
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Additional Information
  • Dorin Ervin Dutkay
  • Affiliation: Department of Mathematics Hill Center-Busch Campus, Rutgers University, Piscataway, New Jersey 08845-8019
  • MR Author ID: 608228
  • Email: ddutkay@math.rutgers.edu
  • Palle E. T. Jorgensen
  • Affiliation: Department of Mathematics The University of Iowa, 14 MacLean Hall, Iowa City, Iowa 52242-1419
  • MR Author ID: 95800
  • ORCID: 0000-0003-2681-5753
  • Email: jorgen@math.uiowa.edu
  • Received by editor(s): January 23, 2005
  • Received by editor(s) in revised form: February 2, 2005
  • Published electronically: March 24, 2005

  • Dedicated: Dedicated to the memory of Shizuo Kakutani
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Conform. Geom. Dyn. 9 (2005), 24-45
  • MSC (2000): Primary 42C40, 42A16, 42A65, 43A65, 46G15, 47D07, 60G18
  • DOI: https://doi.org/10.1090/S1088-4173-05-00135-9
  • MathSciNet review: 2133804