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Transactions of the American Mathematical Society

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Smooth classification of geometrically finite one-dimensional maps

Author: 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 $C^{1}$-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

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).
Article copyright: © Copyright 1996 American Mathematical Society