C^k Conjugacy of 1-D Diffeomorphisms with Periodic Points
Author(s)
Young, Todd R.
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Abstract
It is shown that the set of heteroclinic orbits between two periodic orbits of saddle-node type induces a functional modulus. For one-dimensional C^2 diffeomorphisms with saddle-node periodic points, two such diffeomorphisms are C^2 conjugated if and only if the moduli of their heteroclinic orbits are the same. The modulus is related to the global bifurcation associated with disappearance of a saddle-node point. An equivalent modulus is given for C^k diffeomorphisms with hyperbolic periodic points, and it is shown that this modulus is an invariant of C^k conjugation. However, in this case the modulus alone is sufficient to guarantee conjugacy only in a limited sense.
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The author was partially supported by AFOSR grant #F49620-93-1-0147.
Date
1995-06-05
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