Additional files for the article

PHASE PORTRAITS OF THE FAMILIES V TO X FOR THE QUADRATIC POLYNOMIAL DIFFERENTIAL SYSTEMS

Joan C. Artés, Lorent Cairó and Jaume Libre

If we want to classify a large number of objects, we normally have to divide the set into a few subsets and then classify these subsets one by one. In the study of phase portraits of quadratic systems, different divisions have been tried and some subsets of each division have been classified. So far, no division has been efficient enough to allow a complete classification. In this article we present the most advanced study based on one of these divisions. Specifically, we study a division proposed in [18] which divides quadratic systems into ten different normal forms with six parameters. We will provide the complete classification of phase portraits for six of these normal forms. Altogether with [1], in which a seventh normal form has been studied, we bring together all the current knowledge on this division. Unfortunately the three remaining normal forms are not easy to reduce to simpler forms that allow their complete study.

The proof to check each one of the branches of the Riccati tree and determine to which family belongs, is long and mechanical.

Thus, we have decided to open a web page where we include all those files that one cannot include in the paper, so that the reader may download freely for better understanding and possibly further research. We will keep this page for as long as possible but presumably not indefinitely.

We do not add here the paper due to the copyright, but we place only the Mathematica file in the zipped form to reduce space.

Please note that the file is very large and may take a lot to download. It is consequently even bigger once unzipped. We have added the size of the files both zipped and unzipped so to warn you before downloading.

Mathematica file (17176Kb/1890Kb)