Asymptotics in dynamics, geometry and PDEs ; Generalized by Costin O., et al. (eds.)

By Costin O., et al. (eds.)

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Extra info for Asymptotics in dynamics, geometry and PDEs ; Generalized borel summation. / Vol. I

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These invariants, together with the multiplicity and the index, are the sought complete system of holomorphic invariants. In case λ has modulus one but it is not a root of unity, the map is called “elliptic”. In such a case the germ is always formally linearizable, but, as strange as it might be, it is holomorphically linearizable if and only if topologically linearizable (and this last condition is related to boundedness of the orbits in a neighborhood of 0). Writing λ = e2πiθ , Àrst Siegel and later Bruno and Yoccoz [42] showed that holomorphic linearization depends on the arithmetic properties of θ ∈ R.

M, might be roots of unity, such a normal form is the exact analogue of the formal normal form 30 Filippo Bracci for parabolic germs in C. In fact, a one-resonant germ acts as a parabolic germ on the space of leaves of the formal invariant foliation {z α = const} and that is the reason for this parabolic-like behavior. Let F be a one-resonant non-degenerate diffeomorphism with respect to the eigenvalues {λ1 , . . , λm }. We say that F is parabolically attracting with respect to {λ1 , . .

4 Holomorphic/meromorphic inputs F. Examples . 158 Application to some knot-related power series . . . 2 Two contingent ingress factors . . . . 3 Two original generators Lo and Loo . . 4 Two outer generators Lu and Luu . . . 5 Two inner generators Li and Lii . . . 6 One exceptional generator Le . . . . 8 Computational veriÀcations . . . . 10 General tables . . . . . . . . . . 1 Main formulas . . . . . . . . 2 The Mir mould . . . . . . . . 3 The mir transform: from − g to −h .

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