A starting condition approach to parameter distortion in generalized renormalization

We control parameter distortion in the generalized renormalization procedure provided a certain set of starting conditions is satisfied. This allows us to prove that for aC∞ — open set of unimodal families, almost all parameters inside an interval present either stochastic dynamics or a renormalizat...

Full description

Saved in:
Bibliographic Details
Published in:Qualitative theory of dynamical systems 2001, Vol.2 (2), p.221-288
Main Author: Colli, Eduardo
Format: Article
Language:English
Subjects:
Distortion
Parameters
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We control parameter distortion in the generalized renormalization procedure provided a certain set of starting conditions is satisfied. This allows us to prove that for aC∞ — open set of unimodal families, almost all parameters inside an interval present either stochastic dynamics or a renormalization (in the classical sense). Moreover, easy consequences are that renormalization happens densely on this interval and stochastic behaviour with positive measure. A wide range use of this approach would rely mostly on proving that the starting conditions are satisfied for general families.
ISSN:1575-5460
1662-3592
DOI:10.1007/BF02969343