Geodesic
Conjugation to a shift and the splitting of invariant manifolds
Applicationes Mathematicae, Tome 24 (1997) no. 2, pp. 127-140.

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We give sufficient conditions for a diffeomorphism in the plane to be analytically conjugate to a shift in a complex neighborhood of a segment of an invariant curve. For a family of functions close to the identity uniform estimates are established. As a consequence an exponential upper estimate for splitting of separatrices is established for diffeomorphisms of the plane close to the identity. The constant in the exponent is related to the width of the analyticity domain of the limit flow separatrix. Unlike the previous works the cases of non-area-preserving maps and parabolic fixed points are included.
DOI : 10.4064/am-24-2-127-140
Keywords: normal form, separatrix splitting, finite-difference equation

Vassiliĭ Gelfreich 1

1 
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Vassiliĭ Gelfreich. Conjugation to a shift and the splitting of invariant manifolds. Applicationes Mathematicae, Tome 24 (1997) no. 2, pp. 127-140. doi : 10.4064/am-24-2-127-140. http://geodesic.mathdoc.fr/articles/10.4064/am-24-2-127-140/

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