Improved convergence estimates for the Schröder–Siegel problem View Full Text


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Article Info

DATE

2015-08

AUTHORS

Antonio Giorgilli, Ugo Locatelli, Marco Sansottera

ABSTRACT

We reconsider the Schröder–Siegel problem of conjugating an analytic map in C in the neighborhood of a fixed point to its linear part, extending it to the case of dimension n>1. Assuming a condition which is equivalent to Bruno’s one on the eigenvalues λ1,…,λn of the linear part, we show that the convergence radius ρ of the conjugating transformation satisfies lnρ(λ)≥-CΓ(λ)+C′ with Γ(λ) characterizing the eigenvalues λ, a constant C′ not depending on λ and C=1. This improves the previous results for n>1, where the known proofs give C=2. We also recall that C=1 is known to be the optimal value for n=1. More... »

PAGES

995-1013

References to SciGraph publications

  • 1870-06. Ueber iterirte Functionen in MATHEMATISCHE ANNALEN
  • 1999. A Classical Self-Contained Proof of Kolmogorov’s Theorem on Invariant Tori in HAMILTONIAN SYSTEMS WITH THREE OR MORE DEGREES OF FREEDOM
  • 2014-08. On the convergence of an algorithm constructing the normal form for elliptic lower dimensional tori in planetary systems in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 2002. Analytic linearization of circle diffeomorphisms in DYNAMICAL SYSTEMS AND SMALL DIVISORS
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    http://scigraph.springernature.com/pub.10.1007/s10231-014-0408-4

    DOI

    http://dx.doi.org/10.1007/s10231-014-0408-4

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    https://app.dimensions.ai/details/publication/pub.1011031562


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