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Disintegration of projective measures

Author(s): Dorin Ervin Dutkay; Palle E. T. Jorgensen
Journal: Proc. Amer. Math. Soc. 135 (2007), 169-179.
MSC (2000): Primary 42C40, 42A16, 42A65, 43A65, 46G15, 47D07, 60G18
Posted: June 22, 2006
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Abstract: In this paper, we study a class of quasi-invariant measures on paths generated by discrete dynamical systems. Our main result characterizes the subfamily of these measures which admit a certain disintegration. This is a disintegration with respect to a random walk Markov process which is indexed by the starting point of the paths. Our applications include wavelet constructions on Julia sets of rational maps on the Riemann sphere.

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Additional Information:

Dorin Ervin Dutkay
Affiliation: Department of Mathematics, Hill Center-Busch Campus, Rutgers, The State University of New Jersey, 110 Frelinghuysen Road, Piscataway, New Jersey 08854-8019
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
Email: jorgen@math.uiowa.edu

DOI: 10.1090/S0002-9939-06-08469-3
PII: S 0002-9939(06)08469-3
Keywords: Measures, projective limits, transfer operator, martingale, fixed-point
Received by editor(s): August 16, 2004
Received by editor(s) in revised form: July 29, 2005
Posted: June 22, 2006
Additional Notes: This work was supported in part by NSF grant DMS 0457491
Communicated by: David R. Larson
Copyright of article: Copyright 2006, American Mathematical Society

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