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Smooth classification of geometrically finite one-dimensional maps
Author(s):
Yunping
Jiang
Journal:
Trans. Amer. Math. Soc.
348
(1996),
2391-2412.
MSC (1991):
Primary 58F03, 58F19, 58F34, 30F35
MathSciNet review:
1321579
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Abstract:
The scaling function of a one-dimensional Markov map is defined and studied. We prove that the scaling function of a non-critical geometrically finite one-dimensional map is Hölder continuous, while the scaling function of a critical geometrically finite one-dimensional map is discontinuous. We prove that scaling functions determine Lipschitz conjugacy classes, and moreover, that the scaling function and the exponents and asymmetries of a geometrically finite one-dimensional map are complete  -invariants within a mixing topological conjugacy class.
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Additional Information:
Yunping
Jiang
Affiliation:
Department of Mathematics, Queens College of CUNY, Flushing, New York 11367
Email:
yungc@yunping.math.qc.edu, yungc@qcunix.acc.qc.edu
DOI:
10.1090/S0002-9947-96-01487-0
PII:
S 0002-9947(96)01487-0
Received by editor(s):
April 28, 1992
Received by editor(s) in revised form:
March 6, 1995
Additional Notes:
The author is partially supported by PSC-CUNY awards (6-64053 and 6-65348) and an NSF grant (DMS-9400974).
Copyright of article:
Copyright
1996,
American Mathematical Society
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