Hostname: page-component-6898cfcb55-th4rj Total loading time: 0 Render date: 2026-11-11T14:30:19.185Z Has data issue: false hasContentIssue false
  • English
  • Français

Limit at resonances of linearizations of some complex analytic dynamical systems

Published online by Cambridge University Press:  01 August 2000

ALBERTO BERRETTI,
STEFANO MARMI and
DAVID SAUZIN
ALBERTO BERRETTI
Affiliation:
Dipartimento di Matematica, II Università di Roma (Tor Vergata), Via della Ricerca Scientifica, 00133 Roma, Italy and INFN, Sez. Tor Vergata (e-mail: berretti@roma2.infn.it)
STEFANO MARMI
Affiliation:
Dipartimento di Matematica ‘U. Dini’, Università di Firenze, Viale Morgagni 57a, 50134 Firenze, Italy and INFN, Sez. Firenze (e-mail: marmi@udini.math.unifi.it)
DAVID SAUZIN
Affiliation:
Astronomie et systèmes dynamiques, CNRS – Bureau des longitudes, 77, avenue Denfert-Rochereau, 75014 Paris, France (e-mail: sauzin@bdl.fr)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

We consider the behaviour near resonances of linearizations of germs of holomorphic diffeomorphisms of $({\Bbb C},0)$ and of the semi-standard map.

We prove that for each resonance there exists a suitable blow-up of the Taylor series of the linearization under which it converges uniformly to an analytic function as the multiplier, or rotation number, tends non-tangentially to the resonance.This limit function is explicitly computed and related to questions of formal classification, both for the case of germs and for the case of the semi-standard map.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 20 , Issue 4 , August 2000, pp. 963 - 990
Copyright
2000 Cambridge University Press