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Conjugation to a shift and the splitting of invariant manifolds

100%

Gelfreich V. G.

Applicationes Mathematicae

1996-1997

tom 24

nr 2

127-140

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.

Ograniczanie wyników

1 Applicationes Mathematicae

1 Gelfreich V. G.

1 1997

Wyniki wyszukiwania

Conjugation to a shift and the splitting of invariant manifolds