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- W2322671738 abstract "We reconsider the Poincaré-Siegel center problem, namely the problem of conjugating an analytic system of differential equations in the neighbourhood of an equilibrium to its linear part $Lambda=diag(lambda_1,ldots,lambda_n)$. If the linear part is non--resonant we show that the convergence radius $r$ of the conjugating transformation satisfies $log r(Lambda )ge -CB+C'$ with $C=1$ and a constant $C'$ not depending on $Lambda$. The convergence condition is the same as the Bruno condition since $B = -sum_{rge 1}2^{-r}logalpha_{2^r-1}$, where $alpha_r = min_{0le sle r} beta_r$ for $rge 0$ and $beta_r = min_{j=1,ldots,n} min_{kinZ_+^n,|k|=r+1}$ <b>|</b> < k, $lambda$ > $- lambda_j$<b>|</b>. Our lower bound improves the previous results for $ngt 1$, where the known proofs give $C=2$. We also recall that $C=1$ is known to be the optimal value for the discrete time version of the center problem when $n=1$, namely the linearization problem for germs of holomorphic maps when the eigenvalue of the fixed point is on the unit circle." @default.
- W2322671738 created "2016-06-24" @default.
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- W2322671738 date "2010-01-01" @default.
- W2322671738 modified "2023-10-13" @default.
- W2322671738 title "Convergence radius in the Poincaré-Siegel problem" @default.
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- W2322671738 doi "https://doi.org/10.3934/dcdss.2010.3.601" @default.
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