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$C^k$ conjugacy of 1-d diffeomorphisms
with periodic points


Author: Todd R. Young
Journal: Proc. Amer. Math. Soc. 125 (1997), 1987-1995
MSC (1991): Primary 34C35, 58C25
MathSciNet review: 1372046
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Abstract: It is shown that the set of heteroclinic orbits between two periodic orbits of saddle-node type induces functional moduli which are completely contained in a new `transition map'. For one-dimensional $C^2$ diffeomorphisms with saddle-node periodic points, two such diffeomorphisms are $C^2$ conjugated if and only if the transition maps of their heteroclinic orbits are the same. An equivalent transition map is given for $C^k$ diffeomorphisms with hyperbolic periodic points, and it is shown that this transition map is an invariant of $C^k$ conjugation. However, in this case the transition map alone is sufficient to guarantee conjugacy only in a limited sense.


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Additional Information

Todd R. Young
Affiliation: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332-0160
Address at time of publication: Department of Mathematics, Northwestern University, Evanston, Illinois 60208-2730
Email: young@math.nwu.edu

DOI: https://doi.org/10.1090/S0002-9939-97-03783-0
Keywords: Smooth conjugacy, global conjugacy
Received by editor(s): June 14, 1995
Received by editor(s) in revised form: January 9, 1996
Additional Notes: The author was partially supported by AFOSR grant #F49620-93-1-0147.
Communicated by: Mary Rees
Article copyright: © Copyright 1997 American Mathematical Society