Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-28T07:01:23.020Z 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: [email protected])
STEFANO MARMI
Affiliation:
Dipartimento di Matematica ‘U. Dini’, Università di Firenze, Viale Morgagni 57a, 50134 Firenze, Italy and INFN, Sez. Firenze (e-mail: [email protected])
DAVID SAUZIN
Affiliation:
Astronomie et systèmes dynamiques, CNRS – Bureau des longitudes, 77, avenue Denfert-Rochereau, 75014 Paris, France (e-mail: [email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)