Improved convergence estimates for the Schröder-Siegel problem
| LEADER | caa a22 4500 | ||
|---|---|---|---|
| 001 | 605496374 | ||
| 003 | CHVBK | ||
| 005 | 20210128100536.0 | ||
| 007 | cr unu---uuuuu | ||
| 008 | 210128e20150801xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s10231-014-0408-4 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10231-014-0408-4 | ||
| 245 | 0 | 0 | |a Improved convergence estimates for the Schröder-Siegel problem |h [Elektronische Daten] |c [Antonio Giorgilli, Ugo Locatelli, Marco Sansottera] |
| 520 | 3 | |a We reconsider the Schröder-Siegel problem of conjugating an analytic map in $$\mathbb {C}$$ C in the neighborhood of a fixed point to its linear part, extending it to the case of dimension $$n> 1$$ n > 1 . Assuming a condition which is equivalent to Bruno's one on the eigenvalues $$\lambda _1,\ldots ,\lambda _n$$ λ 1 , ... , λ n of the linear part, we show that the convergence radius $$\rho $$ ρ of the conjugating transformation satisfies $$\ln \rho (\lambda )\ge -C\Gamma (\lambda )+C'$$ ln ρ ( λ ) ≥ - C Γ ( λ ) + C ′ with $$\Gamma (\lambda )$$ Γ ( λ ) characterizing the eigenvalues $$\lambda $$ λ , a constant $$C'$$ C ′ not depending on $$\lambda $$ λ and $$C=1$$ C = 1 . This improves the previous results for $$n> 1$$ n > 1 , where the known proofs give $$C=2$$ C = 2 . We also recall that $$C=1$$ C = 1 is known to be the optimal value for $$n=1$$ n = 1 . | |
| 540 | |a Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2014 | ||
| 690 | 7 | |a Small divisors |2 nationallicence | |
| 690 | 7 | |a Linearization |2 nationallicence | |
| 690 | 7 | |a Diophantine conditions |2 nationallicence | |
| 690 | 7 | |a Normal forms |2 nationallicence | |
| 700 | 1 | |a Giorgilli |D Antonio |u Dipartimento di Matematica, Università degli Studi di Milano, Via Saldini 50, 20133, Milan, Italy |4 aut | |
| 700 | 1 | |a Locatelli |D Ugo |u Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata”, Via della Ricerca Scientifica 1, 00133, Rome, Italy |4 aut | |
| 700 | 1 | |a Sansottera |D Marco |u Département de Mathématique, University of Namur & NAXYS, Rempart de la Vierge 8, 5000, Namur, Belgium |4 aut | |
| 773 | 0 | |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/4(2015-08-01), 995-1013 |x 0373-3114 |q 194:4<995 |1 2015 |2 194 |o 10231 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10231-014-0408-4 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10231-014-0408-4 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Giorgilli |D Antonio |u Dipartimento di Matematica, Università degli Studi di Milano, Via Saldini 50, 20133, Milan, Italy |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Locatelli |D Ugo |u Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata”, Via della Ricerca Scientifica 1, 00133, Rome, Italy |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Sansottera |D Marco |u Département de Mathématique, University of Namur & NAXYS, Rempart de la Vierge 8, 5000, Namur, Belgium |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/4(2015-08-01), 995-1013 |x 0373-3114 |q 194:4<995 |1 2015 |2 194 |o 10231 | ||