If you are experiencing problems downloading PDF or HTML fulltext, our helpdesk recommend clearing your browser cache and trying again. If you need help in clearing your cache, please click here . Still need help? Email help@ingentaconnect.com

Darboux Linearization and Isochronous Centers with a Rational First Integral

The full text article is not available for purchase.

The publisher only permits individual articles to be downloaded by subscribers.

Abstract:

In this paper we study isochronous centers of polynomial systems. It is known that a center is isochronous if and only if it is linearizable. We introduce the notion of Darboux linearizability of a center and give an effective criterion for verifying Darboux linearizability. If a center is Darboux linearizable, the method produces a linearizing change of coordinates. Most of the known polynomial isochronous centers are Darboux linearizable. Moreover, using this criterion we find a new two-parameter family of cubic isochronous centers and give the linearizing changes of coordinates for centers belonging to that family. We also determine all Hamiltonian cubic systems which are Darboux linearizable. In the second part of this work we restrict to the study of isochronous centers having a rational first integral. We prove that, under certain conditions, the cycle vanishing at the isochronous center is either zero homologous in the closure of a generic fiber, or the function obtained from the first integral by eliminating the indeterminacy points has several critical points in the singular fiber passing through the isochronous center.

Document Type: Research Article

Affiliations: Laboratoire de Topologie, UMR 5584 du CNRS, Universite de Bourgogne, France

Publication date: March 1, 1997

Related content

Tools

Favourites

Share Content

Access Key

Free Content
Free content
New Content
New content
Open Access Content
Open access content
Subscribed Content
Subscribed content
Free Trial Content
Free trial content
Cookie Policy
X
Cookie Policy
ingentaconnect website makes use of cookies so as to keep track of data that you have filled in. I am Happy with this Find out more